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AN 

ELEMENTARY TREATISE 



ON 



LOGIC; 



INCLUDINa 

PAKT I. ANALYSIS OF FORMULA-PART IL METHOD. 

WITH AN 

APPENDIX OF EXAMPLES 

FOB ANALYSIS AND CRITICISM. 
• AND 

A COPIOUS INDEX OF TERMS AND SUBJECTS. 



DESIGNED FOR THE USE OF SCHOOLS AND COLLEGES AS WELL AS FOR PRIVATE 

STUDY AND USE. 



BY 

W. D. WILSON, D. D., 

TRINITY PK0FES80R OF CHRISTIAN ETHICS, AND PROFESSOR OF LOGIC, OF XNTELLKCTXTAI 
PHILOSOPHY, AND OF HISTORY IN HOBART FREE COLLEGE, 
AT GENEVA, WESTERN NEW YORK. 



" LoGic—the Mathematics of Thought." — Cousin. 

NEW YORK : 
D. APPLETON AND COMPANY, 

346 «fe 348 BEOADWAY. 
LONDON: 16 LITTLE BRITAIN. 

M.DCCC.LVI. 



*v\ 



^^if' 



30^Z67 



Entered according to Act of Congress, in the year 1856, 

By D. APPLETON & COMPANY, 

In the Clerk's Office of the District Court of the United States for the Southern 
District of New York. 

. a — 

By lrazu#Br f^om 
Pat. Office L^. 

AiyrH 1^14. 









PREFACE 



ft 



r' The following work has grown out of my necessities and 
Li;/ experience as a teacher. When, several years ago, I 
^^'ited a professorship, the "' -^--s of ^hich required me to 
I' le Logic, I could nowhere find a text-book that seemed to 
uiw tO satisfy the demands of the science. 

^or was this feeling peculiar to myself. Mr. Thompson, 
\ hid excellent work on " The Necessary Laws of Thoughtj^^ 
3gins his preface with saying : '* The system of pure Logic, or 
aalytic that has been universally accepted for centuries past, 
.o very defective as an instrument for the analysis of natural 
reasoning. Arguments that commend themselves to any un- 
taught mind as valid and practically important, have no place 
in a system that professedly includes all reasoning whatever ; 
and an attempt to reduce to its technical forms the first few 
pages of any scientific work, has generally ended in failure 
and disgust." 

It would not be difficult to produce almost any amount of 
testimony to the prevalence of a similar feeling with regard to 
the present state of literature in this department of science 
and instruction. 

Of all the efibrts which have recently been made to remedy 
this deficiency, two can be considered as requiring notice in 
this place : that of Prof. De Morgan, and that of Sir Wil- 



IV PKEFACE. 

LiAM Hamilton. The work of Mr. Thompson just referred 
to, is, in its essential features, little, if any thing, more than an 
exposition of Sir William's theory. 

Prof. De Morgan has earned a name in his own depart- 
ment (mathematics), which scholars hereafter will be pleased 
to remember and contemplate. But philosophy, in any of its 
departments, is not his calling. His theory is essentially nu- 
merical. He measures every thing by numerical quantity 
rather than logical. For the purposes of calculation, 2 X, X, 
and X^ are truly different terms, and can no more be substi- 
tuted for each other than X, Y and Z. In this ease, X, Y and 
Z, 2 X and X'^, are assumed as representing simply num- 
ber ; that is, a number of units. Now, units have no indi- 
vidual properties — ^nothing to distinguish one from another. 
Much less have they any separable accidents ; and the only 
difference, therefore, between the sums for which X, Y, Z, &c., 
stand, is in the number of units comprehended in each sum, 
and, consequently, 2 X and X — the one being twice as much 
as the other — are no more the same than X and Y, when they 
represent those different quantities. 

But the words or symbols used in Logic represent the 
conceptions that we form of objects of thought, which are not 
units merely, but individuals also, having each of them insep- 
arable and peculiar properties of their own, upon which not 
only their adequate conception, but any use which we can 
make of that conception in the Formula, whether of mediate 
or of immediate deduction, depends. This fact has been over- 
looked in Prof. De Morgan's Formal Logic, to an extent 
which deprives it of any great value as a system. 

Perhaps the best test of any theory, is a comparison of its 
deductions with the obvious facts and first principles of know- 
ledge. De Morgan refers to an anecdote told of Zerah Col- 
burn, which relates, that having been asked how many black 
beans would make ten white ones, he replied — " ten if you 



PREFACE. V 

skin '^m/" "But," adds De Morgan, "the ten skinned 
beans would not be the same beans as before — except, indeed, 
to those to whom black is white.'' — (p. 54 Formal Logic] 

In the common sense of mankind, the beans are the same 
after being skinned. Philosophy may undertake to correct 
the common sense notions of mankind, but Logic cannot. And 
with how much success philosophy can pursue such an attempt 
we will not now undertake to decide. But in this case it can- 
not succeed. The conclusion, if established, would be gener- 
alized at once — as in fact it ought to be — and we should have 
the doctrine that identity depends upon the separable accidents ; 
and then all science, all knowledge, ethics, and religion, too, will 
be afloat and dissolved into fragments. A man's separable acci- 
dents change from day to day; consequently his identity 
changes. He is not the same man to-day that he was yesterday 
— is not bound to fulfil the contracts of yesterday, or to suffer 
the penalty due to its transgression. 

A theory that not only gives such results, but openly avows 
them, may be safely considered ab absurdo. 

I cannot but regard Sir William Hamilton's theory as 
equally unfounded. 

Sir William's name is one of the greatest of the present 
century of great names in philosophy. His rank will undoubt- 
edly be in the first class — with Aristotle, Plato, Descartes, 
Locke, and Cousin — the few great names that stud the galaxy 
of history. For an acquaintance with the learning and works 
of others in the department of speculative philosophy, he stands 
unrivalled, and probably will never be surpassed. But I have 
not been able to form any such high estimate of his attempts 
at originality. 

He assumes that there may be affirmative judgments with 
distributed predicates. This is so. But, as I have showr 
(Part I, chap. II, sec. 3. — See also p. 65, ^ 244), this is nevei 
done by the mere force of the affirmative copula. The fact, it 



VI PREFACE. 

fact it be, in any case, must always be indicated by sometbing 
not essential to tbe judgment, and I have provided for all such 
eases — (p. 124, ^498 — see 456). 

But, again, he assumes that there may be negative judg- 
ments with undistributed predicates. To this I have given 
what I think will be found a sufficient answer in p. 67 ^ 254 
and the note. A subject is excluded from a Predicate only 
because it has not the Essentia of the class-conception denoted 
by that predicate. But the Essentia of one part of the individ- 
uals contained in it, can never be different from that of another. 
Hence, whatever would exclude a subject from a part of the 
predicate — that is, the predicate as an undistributed term — 
would exclude it for the whole of the predicate as a distributed 
term. 

If Sir William's theories were correct on these points, 
doubtless we should be obliged to abandon the old nomencla- 
ture altogether and begin anew ; as, indeed, Sir William pro- 
poses to do. But believing as I do, and for the reasons given, 
that his theory of quantification is fundamentally wrong, I 
have adhered to the old doctrine, so modifying the statement 
and exposition of it as to provide for the cases which he had 
regarded as demanding the new theory. 

It will also be observed, that in the following treatise I 
have made more account of Method than recent writers have 
been generally inclined to do. Many of them, in fact, have 
omitted it entirely. Perhaps the manner in which it had 
been treated by the scholastic writers, may serve, in some 
measure, as a justification for the estimate in which the modern 
authors have held that part of Logical Science. But not only 
is it of the utmost importance in itself; there is, moreover, as 
I conceive, no way of obviating the objection to devoting so 
much time as is requisite to the mastery of what Whately and 
others with him who omit method altogether, have included 
in their treatises, without revising that part of Logic which is 



PREFACE. Vll 

properly denoted by .the word Method, and in thus giving a 
practical direction and applicability to the whole study. This 
is what I have attempted to do in the part on Method, and I 
hope that scholars and teachers will agree with me in the esti 
mate I have placed upon the subject. 

If Logic is as Cousin has remarked, '^ the Mathematics of 
thought," it must comprehend not only an analysis of the For- 
mula which we use in thinking, but aiso the methods of the 
successful application of these Formulae, and the discussion of 
Methods will require some consideration of the Matter to 
which they are to be applied, and the faculties by which we 
apply them. 

As the Analytic of Formulae may be compared to Geometry, 
so Method may with equal propriety be compared to Arith- 
metic, Algebra, and the Calculus in pure Mathematics — the 
former treats of Form in Space, considered simply as continu- 
ous quantity; the latter of methods of finding results in dis- 
crete quantity. Such Methods are not only Addition, Sub- 
traction, Multiplication and Division, Involution and Evolu- 
tion, but also the Binomial Theorem, the system of Indetermi- 
nate Coefficients, and all the Methods, in short, of Differentia- 
tion and Integration. Every mathematician knows that the 
truth of the result depends upon two conditions, (1.) that the 
Method be applied to proper matter ; and (2.) that the Methods 
themselves are legitimate. 

I have also provided in the Appendix a liberal supply of 
examples for Praxis. These examples may not be sufficient 
to illustrate every principle and formula, as, from the necessities 
of the case, they are for the most part ultimate parts in them- 
selves, and do not admit of the application of some of those prin- 
ciples which relate to the construction of more comprehensive 
wholes. Our limits will not allow of the insertion of examples 
illustrative of some of the principles of Method which we have 
described. Such examples can be foujad only lu the books and 



VIU PREFACE. 

treatises which are altogether too long to be reprinted here. 
Nor can they be represented in any brief or abstract, in such 
a way as to test the principle or be of use in criticising the 
examples themselves. 

I have also divided these examples into classes, so that, if 
thought best, they may be used as the student progresses in 
the Analysis of Formulae — the first four sections being arranged 
with a view to corresponding divisions of Part I. of this work. 

Among the many analogies between Logic and Grammar, 
no one is more important and striking than that property in 
common from which it results ; that as in the one case, so in the 
other, there is scarcely the possibility of getting a thorough 
knowledge of principles and formula without much experience 
in what in Grammar we call parsing. This practice in Logic 
has come to be called Praxis. It consists in a careful analysis 
of all argumentative sentences with reference to the logical 
connection and sequence of the judgments which they express, 
the methods of argumentation, and the adaptation of the 
Methods to the matter. 

But the very process by which we thus perfect our know- 
ledge of the Principles and Formulae into familiarity with their 
use, is precisely that which we are obliged to practise in all 
cases where we apply our Logic at all in the purposes and uses 
of life. Praxis only makes perfect in the art of using our 
faculties and our knowledge in the wider and more important 
spheres for which our studies are designed to fit us. 

It is, I believe, owing to the neglect of Praxis, together 
with the practical difficulty (which nothing but much practice 
can remove) of putting propositions into a Formal shape, that 
the impression that a large part of the arguments in every book 
to which the mind assents, cannot, nevertheless, be put into 
any one of the known and recognized Formula?, has become so 
general. 

Language seldom expresses all that is in the thoughts, and 



PREFACE. IX 

still more seldom all that is implied in what is actually said. 
Kules of rhetoric and taste would forbid such prolixity, even if 
it were possible. But Logic supposes nothing. It demands 
that all that is in the thought should be fully and explicitly 
stated. And one who has given a thorough logical analysis to 
any production, must of necessity understand it as well as he 
who wrote it, and probably, in nine cases out of ten at least, he 
would really understand it much better. He must understand it 
thoroughly J which is certainly more than can in all casos with 
propriety be said of the author himself. How many Enthy- 
memes are uttered, the suppressed premises of which are wholly 
unknown and unsuspected to him who expresses the Enthy- 
meme ? How many conditionals, the sequences of which are un- 
known to the writer or speaker himself ? But all the latent 
elements of these imperfect arguments must have been brought 
out, stated, and examined by him who has gone through with 
a thorough logical criticism of the production. 

The student and the teacher likewise will probably find the 
chapter on Methods of instruction the least full and satisfac- 
tory of any. The reason for this is assigned in the chapter 
itself. I could not make it full and satisfactory without going 
further than unity of plan would permit into the department of 
Rhetoric, nor (waiving that objection), could I go into the 
subject so fully as such a modification of my general subject 
would require, without expanding the volume beyond all reason- 
able bounds. And, after much deliberation, I have decided to 
send it out as it is, regarding it as the best that I can make 
of the matter now and under the present circumstances. Such 
as it is, however, I trust that it will not be found unworthy 
of attention and diligent study. 

In conclusion, I wish to express my decided conviction 
not only of the usefulness of Logic as an instrument, but also 
that it needs more attention and more time than any work on 
the subject hitherto given to the public, has seemed to me to 



X PKEFACE. 

deserve. It is to all the speculative sciences, every branch of 
knowledge except mathematics, what arithmetic and algebra 
are to the Mathematics themselves — as an instrument in con- 
structing those sciences — and it is as necessary as grammar it- 
self to rhetoric, and all the departments of literary criticism, 
dialectics, and oratory. 

In speaking thus of the importance of the science, and of 
a thorough education in it, I am not of course advocating the 
introduction of its technicalities and Formulae into public speak- 
ing and writing ; the analogy of grammar and rhetoric holds 
here also. No one, in speaking or writing, stops to parse his 
words, or to name every figure of speech which he uses, or every 
rule of rhetoric which he may have had in mind when he wrote 
or spoke. No more is it expected that the same thing should 
be done in regard to Logic. Here, as elsewhere, it may be 
said, the greatest art is to conceal art — to write with a perfect 
knowledge of all the terms and principles of the science of 
writing, and yet never thrust them forward in such a way as to 
be offensive to good taste, or vexatious to the reader. 

To reason logically is not the same as to reason formally. 
All good reasoning is of necessity logical, just as all good writ- 
ing must fulfil * the rules and requirements of grammar and 
rhetoric. But it is not expected that the arguments will 
always be stated in the precise forms that are given in this 
book ; nor that all that is requisite to their completion shall 
be expressly given. Logic supposes nothing. It allows of no 
omissions — no ellipses. On the contrary, rhetoric, good taste, 
brevity, and more than all, the scantiness of thought in the mind 
of the speaker, make this necessary. Logic teaches what these 
omissions are, how they are to be restored or produced to 
fill up the vacancies. And thus the reasoning fulfils the For- 
mula — becomes formal — or, as it is commonly but very impro- 
perly called, logical. But nothing can be more idle than the 
objection to the study of Logic, based upon the fact that its 



PREFACE. XI 

FormulaB and technicalities do not appear, and are not expected 
to appear, in the written or published discourse of ordinary 
life. One might with as much propriety object to the study 
of the Binomial Theorem, on the ground that in equations of 
the second degree, we seldom or never find the square of the 
Binomial complete. Without these Formulae and technicalities, 
what is written and said can never be comprehended or intel- 
ligibly discussed. 

But, after all, it must be distinctly considered that Logic, 
like the pure Mathematics, is only a means and not an end. The 
pursuit of the study may be valuable as a discipline. Its 
results will be of great service to any one who has thoroughly 
comprehended them. But if one looks to its Formulae as a 
substitute for common sense in the common affairs of life, or 
of investigation in the higher pursuits of literature and science, 
or of patient and laborious thought anywhere, he will be sadly 
disappointed. 

W. D. WILSON. 

Geneva, Dec, 1855. 



CONTENTS 



• • • 



PAOB 

Introduction. — Logic Defined ; its Origin, Necessity, and Uses ; its 
Sphere Pointed out, and the Starting Point Ascer- 
tained, 1 



PART I. 

ANALYSIS OF FORMULA. 



CHAPTER I. 



OF TERMS. 



Section I. — Of Conceptions — their Formation, their Object and Rela- 
tions, 9 

II. — Of Substance and Properties — Sphere and Matter of Con- 
ceptions, Essentia, Genus, General and Collective 
Terms, Diflferentia and Species, Individual and Acci- 
dents, 13 

m. — Of the whole and its Parts, 21 

I. — Of Quantity, three kinds, 22 

II. — Of Division, thkek kinds, 24 






XIV CONTENTS. 



PAGB 



Sec. IV. — The Relation of Cause and Effect, 29 

V. — Of Difference^ Identity, Resemblance, and Analogy, 32 

VI. — Of Definition and Description, 33 

VII. — Of the Quality of Terms — General, Specific, Synonymous, 
Analogous, Incompatible, Positive, Negative, and Priva- 
tive, 34 

VIII. — Of the Quantity of Terms — Numerals, Ordinals, Positive 
and Negative, Infinite, Comparatives and Superlatives, 

Distributed and Undi^ributed, 38 

IX. — Of the Opposition of Terms — Relative, Contrary, Sub- 
contrary, Contradictory, 40 



CHAPTER n. 

OP PROPOSITIONS, 

Section I. — Of Judgments — Scope, Kinds, Categorical, Conditional, 
Disjunctive, Hypothetical, Relative or Comparative, and 

Probable, 43 

IT. — Of the Terms in a Proposition — how Placed, Propositions 

Resolvable into Terms, 46 

in. — Of the Copula — its Force, Forms, Effects, and Classifi- 
cation, 48 

IV. — Of the Adequacy of Propositions, 55 

V. — Of the Quantity of Judgments — Individual, Particular, 

and Universal Judgments, 59 

VI. — Of the Quality of Judgments, 61 

VII. — Of the Modality of Judgments, 61 

VIII. — Of the Four Cardinal Propositions — Universal Afiimia- 
tive. Universal Negative, Particular Affirmative, and 

Particular Negative, 62 

IX. — Of the Distribution of Terms in Judgments, 6-1 

X. — Of Immediate Inference, 69 

1. — By the Opposition of Judgments, 70 

II. — By Permutation or Contra- Position, 71 

III. Byconversion, 74 

IV.— By Substitution op Terms, 76 



I 



\ 



CONTENTS. XV 

PAGB 

Sec. XI. — Of Complex Propositions — Modals, Explicative, Differ- 
ential, Exceptional, Exclusive, Conditional, and Pro- 
trusive, « 77 

XII. — Of Compound Propositions — Express and Implied, Copu- 
lative Causal, Discretive, Conditional, and Disjunctive, 

Exceptives, and Exclusives, 80 

Xin. — Of Comparative Judgments, 84 

XrV. — Of Probable Judgments — The Calculation of Chances, 

Antecedent and Special Probabilities, 87 

XV. — Of Conditional Judgments — The Sequence, Complex Se- 
quences, Compound and Continuous Conditionals, 91 

XVI. — Of Disjunctive Judgments and Excluded Middle, 97 

XVII. — Of the Grounds of Affirmation — Identity and Contradic- 
tion, Sufficient Cause, and Excluded Middle 102 



CHAPTER m. 



OF SYLLOGISMS. 



Section I. — Classification of Syllogisms — Names of the Terms, and 

Parts in Pure Categorical Syllogisms, 106 

n. — Of Pure Categorical Syllogisms^ 110 

I. — Of the Figure of Syllogisms, 110 

II. — Of the Mood of Syllogisms, 115 

III. — Application OF Moods TO THE Figures, 118 

in. — Of Indirect Conclusions^ 123 

rV. — Of the Conversion of Syllogisms — Ostensive Reduction, 

and Reductio ad impossibile, 121 

V. — Of Complex Syllogisms — Change of Modals and Proten- 

sive Quantity, 131 

VI. — Of Compound Syllogisms, or Sorites, the Reduction of 

Sorites to Simple Categoricals, 138 

Vn. — Of the Incomplete Formulce^ or Enthymemes, Inductive 

and Cumulative Formula, 142 

Vni. — Of Epichirema, Pro-syllogism s, and Epi -syllogisms, 148 

IX. — Of Comp oimd Judgments in Syllogisms, 149 



XVI CONTENTS. 

PAGE 

Sec. X. — Of Comparative Syllogisms — 

L~BiMPLE Comparatives, 152 

II. — Comparatives in wniCH the Difference of Intensity 

IS Eegarded as a Cause, 155 

III. — Comparatives, Manner, &c., 156 

XL — Of Probable Syllogisms, the Effect of Discrete Quantity 
on Logical, and the Combination of Independent Pro- 
babilities, 157 

XII. — Of Conditional Syllogisms — their Completion, 170 

Xlll. — Of Disjunctive Syllogisms — Comprehensive and Divisive 175 
XIV,— Of the Dilemma, 179 



CHAPTER IV. 

OF FALLACIES. 

Section I. — Of the Ignoratio Elenchi^ 185 

n. — Of the Petitio Principii, 186 

in. — Of the Ambiguous Middle, 189 

rV. — Of Division and Composition, 190 

V. — Of Accidents and Quid, 191 



i 



PAKT II. 

LOGICAL METHODS. 

CHAPTER I. ' 
OF THE ELEMENTS OF METHOD. 

Section I. — Of Method in General, 194 

II. — Of Order as an Element of Method, 196 

III. — Of the Ideas which Determine Methods, 198 



CONTENTS. XVli 

PAOI 

Sec. IV. — Of the Matter of Logical Methods — Analytical and Syn- 
thetic Judgments, Necessary and Contingent Matter, 
Class-Conceptions, Judgments d priori and d, posteriori, 
Material and Implied Properties, Formal and Modal 
Properties, Absolute, Physical, and Moral Certainty, 
Analysis, Synthesis, Truth, Opinion, Hypothesis, 
Theory, and Conjecture, 202 



CHAPTER II. 

METHODS OF INVESTIGATION. 

Section I. — Of Investigation — The finding of Predicates, 219 

II. — Of Observation and Testimony — the External Senses, 
Consciousness, Experiment, the use of Hypotheses, and 

of Testimony, 

in. — Of Measurement and Calculation — Methods of Obtain- 
ing Wholes from Parts and Parts from Wholes, 232 

rV. — Of Average and Exclusion, or the Abscissio Injiniti, 237 

V. — Of Analysis — The Analysis of Conceptions and of Ob- 
jects, 243 

VI. — Of Induction and Analogy — Several forms of Induction, 249 
VII. — Of Elimination^ Causes and Antecedents — Causality Im- 
plies Substance, Methods of Elimination, 259 



CHAPTER m. 

METHODS OF PROOF AND REFUTATON. 

Section I. — Of Proo/— Direct and Indirect Methods,. ^ 275 

n. — Of Demonstration, 281 

III.— 0/ Deduction, 290 

IV. — Of the Argument from Authority — Principles of Inter- 
pretation, 293 

V. — Of the Appeal to Facts, by way of Induction, the Uni- 
formity of Nature, Final Causes, Example, Analogy, 
and Circumstantial Facts, 303 



XVm CONTENTS. 

PAGE 

Sec. VI. — Of Progressive Approach, 324 

Vn. — Of the Argumentum ad Jgnorantiam, 326 

TUl,— Of Refutation, three Methods 328 

IX.— Of Direct Refutation, 329 

X. — Of Indirect Refutation, 333 

XI. — Of Personal Refutations, ad hominem, ad verecitndiam, 

ad invidiam, 336 



CHAPTER IV. 

METHODS OF INSTRUCTION AND CRITICISM. 

Section I. — Classification of the Sciences — Plato's Classification, 
Aristotle's Scholastic, Bacon's, Locke's, Ampere's and 

Compte's — a new one proposed, 338 

n, — Of the Conveyance of Ideas frcym one Mind to Another — 
as Determining Methods of Instruction, Ideas Con- 
veyed only by Definition and Reconstruction, 347 

III. — Of Definition and Description — Real and Verbal Defini- 
tions, Definition of " Simple Ideas," Ultimate Concep- 
tions, Description Furnishes no Matter for a Concep- 
tion, 349 

rV. — Of Natural and Artificial Classifications — ^Natural 
Classifications made in Cognition, Necessity for Scien- 
tific Classifications, Recurring Species, 356 

V. — Of the Division of the General Subject — Divisions in Pro- 
tensive Extension, in Comprehensive, 360 

VI. — Of the Order in the Treatment — Matter Divided into 
Classes with Reference to the Order of Statements, Or- 
der Stated, Rules for Omission of Matter as Irrelevant 
to the End in View, Necessity for an End or Special 

Aim, 361 

VII. — Methods of Criticism — The Critic's Point of View, the 
Relation of Whole and Parts, Argument and Impres- 
sion, Logical Matter and mere Assertion, Arguments 
and Artifices, Criticism of Terms, Contradictio in Ad- 
jectisj...., 369 



CONTENTS. XIX 



APPENDIX OF EXAMPLES FOR CRITICISM, 

§ 1. Of the Order in Criticising Arguments, 377 

§ 2. Examples in Categorical Syllogisms, 379 

§ 3. Examples in Hypothetical Syllogisms, 382 

§ 4. Examples in Complete and Compound Formulce, 386 

§ 5. Miscellaneous Examples of Formulce and Fallacies, 389 

§6. Examples Involving Questions of Method, 396 

§ 7. Leslie's Short and Easy Method, 401 

§ 8. Webster's Argument in the Girard Will Case, 404 

§ 9. Danas Argument in the Ellsworth School Case, 407 

Index, 411 



LOGIC. 



INTEODUCTION 



1. The word Logic has been used in many different 
senses, and most treatises on the subject have Logic various- 
included matter belonging to widely differ- ^^ defined. 
ent spheres of thought and inquiry. It sometimes de- 
notes the science which explains the laws of thought 
merely. It is sometimes used to denote the art of con- 
vincing and persuading. It has been thought to imply 
the consideration of the means of discovering truth, and 
also the general principles of Method. 

2. Philosophy was in existence and cultivated some 
time before Logic appeared as a distinct philosophy be- 
Science or Art. The reason is obvious. Men ^^e Logic. 
do not seek a Canon of Truth until they feel the danger 
of error, and have reaped the bitter fruits of its expe- 
rience. The earliest schools of Greek Philosophy (and 
of the Hindoo Philosophy we cannot now speak, for 
want of chronological data) — the Ionian and the Pytha- 
gorean — argued and dogmatized without fear or expec- 
tation of contradiction ; they were too sanguine and 
ponfident to feel the need of Logic. 

1 



2 INTRODTJCTION. 

3. But as soon as the doctrines of these two schools 
came into conflict, some Canon, or test, of truth was found 

The origin of ^0 bc ncccssary. Not only terms in which 
^°^^^- to discuss the points at issue, but an in- 

spection of first principles, and of the processes of 
deduction from them, came to be regarded as indis- 
pensable to the discovery of truth, and the proper 
testing of the means by which it may be proved to be 
true. 

4. No system of Logic, however, was formally de- 

veloped and digested until Aristotle. Aris- 
Aiitff °of the totle ^ himself, however, says Zeno the Elea- 

first system. . . i i • i j? V • j^i 

tic, was the mventor of -Logic, or rather 
Dialectics, Aia\€KTLicrj. 

5. As soon, however, as Philosophy had sufficiently 
explored the field which it had to occupy, to form any 
definite idea of what is contained in it, we find Plato 
dividing it into three coordinate branches: — Physic, 

Ethic, and Logic ; f — the former including 
vision^of'^phiio- all of the Natural Sciences ; the second, all 
sophy. ^j^^^ concern the relations and duties of man ; 

and the latter. Logic, the science of mind, and the 
rules by which its activity is to be guided to the proper 
results. 

6. Logic is derived from the Greek A6yo<;y and in 
Logic, how tbe sense used by Plato, it means whatever 

used by Plato, pertaius to the Mind, the Keason, the imma- 
terial power or faculty which is manifested in the 
words and speech of men. Logic was used to denote 
the whole of what, in modern times, has been called 
Intellectual Philosophy, or Metaphysics. 

7. But Intellectual Philosophy or Metaphysics, in 
this broad extent of meaning, includes at least three 
distinct departments of science. 

(1.) Psychology^ as it is called, describing the facts 
of the mind, of which we are immediately conscious ; 

* Sext. Empir. adv. Math. B. vii. c. 1. 
\ Diog. Laert., Prooem. seg. 18. 



INTRODUCTION. 3 

Buch as Sensation, Perception, Abstraction, psychology. 
Conception, Association, Imagination, Memory, Intui- 
tion, Judgment, Inference, &c. 

(2.) Metaphysics proper, which investigates the 
necessary a priori conditions and laws of Metaphysics, 
thought, and the ideas which determine cognition 
and judgment, and those necessary axioms, or first 
principles, which are assumed in all sciences, and 
underlie them, as the ground of their possibility and 
reality. 

And (3.) Logic ; which treats of the relations of 
conceptions to one another ; the deduction Logic in this 
of secondary from primary and intuitive narrower sense. 
judgments, and the laws of Synthesis, by which truths 
are constructed into systems. 

8. The last element of this definition is what has 
usually been called Method; and latterly Method not in- 
there has been a tendency to regard it as a ^^""^^"^ latteriy. 
science by itself. Excluding Method, therefore, from 
our definition, Logic may be defined as the Science of 
Deductive Thinking, 

9. As there may be true and legitimate deductions 
as well as such as are false and delusive. Logic a &«•• 
there must be a Science of deduction, by ^"^*- 
which the true may be distinguished from the false ; 
and the laws and formulas of deduction itself so ex- 
plained and developed, as to enable one to select and 
pursue those methods which lead to right conclusions, 
and avoid those that are fallacious. 

10. But it is necessary for the practical benefits of 
the science, to take some note of language, ^^ relation to 
or the words and signs by which thinking iec^tic8^o?*Rhe- 
is expressed ; of the matter of which we ^°"^- 
think and reason ; and especially of the various ways 
in which the Formulae may be used in the construction 
of what, in popular language, are called Arguments ; 
these form the transition from Logic, as a Science, to 
Logic as an Art. Logic, as an Art, is more properly 
called Dialectics or Rhetoric. It is, of course, with 



ft INTRODUCTION. 

Logic as a Science, that we have chiefly to do in this 
volume. 

11. The purpose which w^e have now before us does 
not lead us to regard Logic as a means of discovery, 

or of so constructing such methods of argu- 
teaches what^u mcntatiou, as are used in speeches and books, 
good reasoning. ^^ ^^ -^^ most succcssful iu a dialcctic point 

of view ; not, in short, to teach directly how to reason 
welly but rather what is good reasoning, and why it 
is so. 

12. In this view, Logic sustains about the same 
relation to public writing and speaking that Grammar 

Logic anaio- docs, or that Moral Science sustains to good 
mar^ Ac^S^^a morals ; the Science of Music to good sing- 
science, jjjg . Qp anatomy and physiology to the prin- 
ciples of health and the practice of Medicine and 
Surgery.* 

13. As in Grammar, for example, we need some 
terms and names, by which to represent the parts of 

speech, and the rules determining the inflec- 
inst?ume]?t ^f tiou and rclatiou of each part to others, and 
en czsm. ^^ ^j^^ wholc sentcncc ; so in Logic we need 
names for each part of a process of thought, and 
rules and laws determining their relation, both for 
the purpose of discussing and analyzing the thoughts 
of others, and to assist in the due expression of our 
own. Without such aids it is impossible to study 
Rhetoric and Oratory, or Psychology and Metaphy- 
sics with much success ; and they are of the greatest 
importance in all departments of study and instruc- 
tion. 

14. There is obviously a distinction between a pro- 
cess of thought and the matter about which the thoughts 

Form and Mat- ^^^ occupicd ; tlic ordcr, arrangement, and 
ter of thinking, dependence of the thoughts upon one another 

* Of course one may speak without knowing Grammar, or sing 
without a knowledge of the scientific principles of harmony and mel- 
ody. But he could speak and sing much better with such knowledge, 
and he could hardly teach or compose without it. 



INTRODUCTION. o 

jnay remain the same, and the matter be different ; and 
vice versa, the matter may remain the same, and the 
order and sequence of the thoughts be different. Hence 
the distinction between the Form of an argument, 
or processes of thought, and the Matter ; the Form 
denotes merely the order, dependence, and arrange- 
ment of the thoughts. Thus, if I say, '^ men are 
mortal, and therefore they should prepare for death ; " 
and " men should prepare for death because they 
are mortal ; " the Matter would be the same in eaclfi 
case, but the form would be different. But if I 
should say, " men are mortal, therefore they should 
prepare for death ; " and " spring is coming, therefore 
we should prepare for summer ; " the Form would be 
the same in both instances, but they would differ m 
matter. 

15. But again, in aiiy continuous process of argu- 
mentation, as in a Speech, an Essay, or a Method. 
Book, these Forms or Formulae may be combined and 
used in different relations, and follow each other in 
different order. Hence, besides tlie Matter and Form 
of an argument, we have to consider also the Method / 
that is, the way in which the Forms are used. Thus, 
if I wish to prove that four times twenty-five is one 
hundred, I may do it by writing twenty-five four 
times, each directly under the other, and then add 
them up I or, by writing it once with a four under 
it, and then "inultiply^ the result will be the same in 
each case, but the Method will be different ; the 
former is the Method of Addition, the latter of Multi- 
plication. 

16. Logic is called Formal, and sometimes Ana- 
lytic, when it investigates the varieties and Formal Logic. 
laws of the Formulae. When it goes farther and in- 
quires into the grounds of the validity of these Formulae, 
it is called Rational / and when it goes one . Rational, 
step farther, and takes into consideration the diversities 
of the various kinds of matter, and the peculiarities in 
the forms of expression by which that matter is repre- 



6 mXRODUCTION. 

sented, and the application of Formulae as modified 
Applied. by the matter, it becomes what we call Ajp- 
plied Logic. 

17. Logic always presupposes, or takes for granted. 
Logic pre- ccrtaiu premises or starting-points ; the 

tmths!^^ ^°"^® truth or falsehood of which it belongs to 
other branches of science to determine. It is concerned 
How far con- "wlth tlic truth of Propositious, only so far as 
trnth^irprop^o^ they are given as resulting from certain 
sitions. others. But the first elements of reasoning, 

the primary facts, it takes from other branches of know- 
ledge, as they have been ascertained and established 
in those branches representing them. It does not un- 
dertake to prove the self-evident axioms or the primary 
facts of science in any department ; but with those 
axioms and facts, given in philosophy and experience, 
it directs and guides the mind at every step, to its most 
remote results, to the highest generalizations, and to 
the most comprehensive truths ; as well as in every 
application of those truths to the practical pui-poses 
of life. 

Logic therefore does not supersede, but rather pre- 
supposes, a knowledge (derived from other sources) 

of the subject matter with which our minds 
laws and^pro^ may bc occuplcd. It simply explains the 

laws by which the mind is guided in arrang- 
ing and combining that matter into scientific systems, 
and in its application to the various purposes and uses 
of life. 

18. Nor, again, does Logic propose a new way for 
doing what we have been accustomed to do in an- 
other. From the earliest development of 

new^wayofrea*^ intcllcct, and the vcry commencement of 
Boning. intellectual activity, the mind has been ac- 

customed to think and to draw inferences, or think 
deductively ; so that we have all been long in the 
practice of Logic, before we begin the study of its 
science. 

19. Those forms and processes in which we proceed 



mTRODUCTION. 'J 

from one thought to another, which depends upon the 
preceding, are called in the popular language Argu 
ments. How long soever or how complicated soever 
they may be, Formulse and Method are thus undistin- 
guished from each other. The Formulae, or syiiogisms 
separate processes, each of which has one subject and 
but one, are called in Logical language, Syllogisms ; 
the word is of Greek origin, and signifies a putting 
together for the sake of a Conclusion. 

20. A Syllogism, therefore, first presents itself to 
our reflective thought as a completed thing ; ^^^e parts of 
having already all of its parts, and most of ^ syiiogism. 
them in their legitimate places, and connected with the 
other parts. Each argument consists of several Pro- 
positions ; one of which we call a Conclu- ^he parts of 
sion^ and the others the Premises ; these ^ ^Proposition. 
Propositions consist most of them of two terms and a 
Copula, One term, called the Sitbject^ de- subject-pre- 
notes that about which we are speaking ; ^^*^^'^' 

the other, called the Predicate^ denotes what Tye say 
of it ; and the Copula is the verb affirming or deny- 
ing the agreement between the Subject and Predicate : 
as A is B, or A is not B. Here " A " is the 
Subject, "^" is the Predicate, and "^5" firmTtfvl' g^d 
and " is not " the Copula ; the former of ^^^^^^''®- 
which is called the Affirmative and the latter the Nega- 
tive Copula. 

21. That act of the mind by which the Copula is 
affirmed or denied, is called a Judgment^ ^ judgment. 
or when expressed in words, a Proposition. ^eSsorcog- 
" A " and " B " are called Terms, and that "^^*«"^- 

in the mind which they represent, is called a Cognition^ 
ox a Conception. 

We come therefore to Conceptions or Cognitions^ as 
the simplest element with which Logic, in 
our use of the word is concerned, and the the ^"starting' 
point of departure with which we must 
commence in the methodical construction of the 
Science. 



8 iNTRODrcnoN. 

22. Logic, however, presupposes some knowledge 
of Psychology, and we must look to that for the expla- 
nation of some of the facts and terms which 
posef *^pJychS- it assumcs as already known. These, how- 
^^' ever, for the sake of completeness, we will 

run over in a very cursory manner. 



PART I. 

ANALYSIS OF FORMULA. 



CHAPTEE I. 

OF TERMS. 

23. Terms are the words or signs by which any 
conception or cognition is expressed, for the Tenns defined, 
purpose of conveying it from one mind to another. 

SECTION I. 
Of Conceptions. 

24. When we look at any object an act of the mind 
ensues, which in psychology is called per- perceptions. 
ceiving — and the result of that act is called a Percep- 
tion. But the mind retains the result of that act 
after the object has been removed from any phy- 
sical connection with us, and the mind can recall it at 
pleasure. In this view of it, that result is called a 
conception or a cognition. 

25. Perception is an instantaneous act, and on 
each occasion, when the same object is pre- ^n instanta- 
sented anew to the senses, we perceive it "^°"^ '^^^^ 
anew, and form anew, or again, a cognition of it. We 
have thus at the second time a new or second per- 

1^ 



10 LOGIC. PART I. [chap. 

ception, which the mind compares with the first, and 
gives the judgment of identity in regard to th^ object 
which occasioned them. 

26. But if the perceptions differ so much or in such 
ways as to imply a difference in any of the insepa- 
rable properties of the object perceived, 

Identity and ^i • j^ • ii t_- ^ T 

diversity of Ob- thc mmd conccivcs the oblects as diverse 

jects perceived, p i ii 

from each other. 

27. In Logic we regard the different cognitions of 
the same object as one and the same cognition, ex- 
cept when we wish to take into considera- 

nitionf ^of The tiou the cliansrcs which the object itself 

same object. -i i^ i i? j.i it 

may undergo, by a change oi those separable 
accidents and modes of existence, which may be 
changed without changing the identity of the object 
itself. 

28. A distinction is sometimes made in the use 
of the words '' cognition'^^ and ''conceptions^'' by which 

Distinction be- ^^ formcr is used to denote the idea of 
uo^^nd^'^co'li- one individual object only : as "a ma^," 
ception. a ^ pen^^'^ &c. ; and conception, the idea of 

a class: as ''mankind^'' " villages ^^'^ '' jpens^'' &c. I 
shall not take pains to adhere to this distinction very 
closely ; although I shall never employ the word 
" cognition " to denote the idea of a class. I shall, 
however, very often use the word " conception " when 
I mean to refer to the idea or cognition of an individual 
thing only. 

29. A conception or a cognition may be adequate or 
inadequate. It is adequate only when it includes, so 

that we may be said to know, all the pro- 
adeqJat?^ 'aSd pcrtics, uscs, purposcs, and the history of the 
ina equate. q^j^^jI; . other wise it is, strictly speaking, in- 
adequate. 

30. No one of the senses by itself and alone can 
ever enable us to form an adequate conception of any 

Diverse sen- objcct. Wc scc its color ; wc smcll its odor ; 
SfteTo an'^airi"- ^c tastc its flavor ; we feel its density and 
quate concep- ]^ smoothuess, &c. Nor can we ever know, 



I.] OF TERMS. SECT. I. 11 

or form an adequate conception, of any considerable 
proportion of the objects with which human knowledge 
is occupied, by any contact of those objects with our 
own senses. Hence we have to rely upon the testimony 
of others, historians, travellers, and observers in every 
department of science, for by far the largest part of 
what we know. 

31. Moreover, there are many objects of thought 
of which we have conceptions, whicli how- conceptions 
ever never have and never can have any o^i^eas. 
connection with the external senses, as means of cog- 
nition ; such as truth, justice, virtue, eternity, &c. 
These objects of thought are sometimes called Ideas, 
and are said to be furnished by the Reason itself. 

32. It would appear that man can have but very 
few, if any, conceptions or cognitions that 

are strictly and absolutely adequate ; and uonVlbsoi^u^eiy 
hence we are accustomed to call those " m- ^ ^'^"**^* 
adequate " only, which are not sufficient for the purpose 
for which the conception itself is used. Thus, if one 
were writing a treatise upon iron, and did not know, 
or have as .a part of his conception of iron, its property 
of becoming magnetized, his conception would be in- 
adequate. But if his object was merely to describe its 
adaptedness to some particular purpose, not at all 
affected by its magnetic properties, his conception 
might be adequate for that purpose ; without includ- 
ing a knowledge of its susceptibility to magnetic in- 
fluences. 

33. Logic requires, and always presupposes, that all 
conceptions whicli are introduced as elements 

of its Formulae, are adequate in this second- how^matS adl- 
ary and limited sense. And if any concep- 
tion is not adequate, it must be rendered so by further 
acquaintance with the object of thought which it repre- 
sents to the mind, and the conception can be conveyed 
adequately to the minds of others by means of defini- 
tions, description, &c. 

34. The objects of which our cognitions are formed, 



12 LOGIC. PART I# [chap. 

are distinguished as possible, impossible^ and real. An 
Objects of object is said to be real when it has an ac- 
m^impofs^t, t^al existence. It is said to be possible when 
and real. j^ jg j^^^ known to have any existence, but is 
nevertheless supposed to have the possibility of exist- 
ing ; thus all realities were merely possible before they 
were brought into actual existence. But an object oi 
thought which can never exist, is called impossible, as 
a triangle with only two sides. 

35. Realities, or things real, have also been distin- 
guished into two classes : the Realities of Being and 

the Realities of Truth, Mind, and all the 

Realities of^ ^ ^''^•1 -j 'ij 

Being and of torms 01 material existence, are considered 
as Realities of Being or Existence. But, 
besides justice, virtue, &c., which exist only as proper- 
ties of some intelligent being; there are also certain 
objects of thought, as time, space, the point, the line, 
&c., and the first axioms of all knowledge, as the 
whole is equal to the sum of its parts, &c., which 
have no substantial existence, and from their very 
nature they can have none. Nor yet are they con- 
sidered as merely the properties of any substance, 
whether material or immaterial. Their reality would 
remain unchanged even if there were no mind in 
existence to comprehend them. They are called Reali- 
ties of Truth. 

36. It has sometimes been said, that we can have 
no conception of the impossible. But we must make 

a distinction between a conception and the 

Conceptions , ,. /» . i»jiT*i'j.i 

of the impossi- coustructiou 01 au image oi the object m the 
mind. An image of the impossible we can- 
not have, but a conception we may have ; for we use 
the word conception to denote any thing of which we 
can speak. If, therefore, we can speak of that which 
is impossible, we can have a conception of it, which 
comprehends all the properties that can be predi- 
cated of it — a conception therefore adequate to all 
the purposes lor which a conception can be needed or 
used. 



I.] OF TERMS. — SECT. H. 13 

37. The objects of thought, of which we form con- 
ceptions or cognitions, are considered as sire- Relations of 
taining several different relations to each conceptions. 
other, upon which deduction depends in several ways ; 
such as Substance and Property, Whole and its Parts, 
Cause and Effect, Identity, Difference^ Resemblance or 
Similarity, Contrariety and Analogy. 

SECTION 11. 

Of Substance and Properties. 

38. By Substance, we mean, that which can be con- 
ceived of as existing by itself {quod substat substance. 
per se). By a Property, an object of thought which 
cannot be conceived to exist, except as in- property, 
hering in some Substance ; thus iron is a substance ; 
hardness is a property of it. 

39. Each Substance must have several properties, 
and may have many. Consequently, any 

1 . , "^ T •^ 1' i \^ Each substance 

subject may nave many predicates; thus, has several pro- 
'' Matter is extended," " Matter is divisi- ^^'^'*'^* 
ble," "Matter is inert," &c. ; — "Iron is hard," 
" Iron is malleable, " " Iron is ductile, " " Iron is 
useful," &c. &c. 

40. Each predicate also may be predicated of more 
than one subject; thus, not only is "Iron Each proper- 
hard,'' but "Lead is hard,'' "Diamond is Z^evlr^A^. 
hard,'' " Oak is hard," &c. '^*^"«- 

41. When a term is thus used as a predicate, it is 
said to he predicated of its subject ; and the predicated, 
subject is said to be in the category denoted by the 
predicate ; thus, " man is mortal'' Here category. 
" mortal " or " mortality " is said to be predicated of 
" man," and " man " is said to be in the category 
" mortal." 

42. Words or terms which may thus be predicated 
of several subjects, are called Predicables or predicabies. 
Categorematic / those which cannot be pre- categorematic 
dicated of more than one subject are called mati<^*^^^**^°' 



14 LOGIC. — PART I. [chap. 

Acategorematie. Such are all words standing for indi- 
vidual objects, proper names, &c. 

43. Any word which expresses an object, or the 
property as belonging to or inhering in its substance, 

is called a concrete term : as " white^^^ 

erins. ^^ i^rj^g^-^ ^(.^ g^^t a word that expresses the 

property considered by itself as an object of thought, 

Abstract terms, is callcd au obstvact term; as " whiteness ^^^ 

'Hength^^^ &c. 

44. But such terms as " white," " long," &c., while 
they c^^note the abstract property, also imply some- 
thins^ that is " white^'' " lonq^'' &c. Hence 

Denotatives ^^ , n j /^ i 

and connota- such tcrms arc called (JoNNOTATrvES, and are 
said to (^^note the property of " length^'' for 
instance, and to connote the body or substance that is 
long. 

45. Every conception is considered as having two 
Sphere and elemcuts, a Sphere and Ma^iter ; or, as it 

Matter of a Con- . .. t. , -x n i * 

ception. IS sometimcs designated, a Uorrvprehension 

and an Intension. 

46. The Sj)here or Convprehension is the number of 
Sphere, individuals included in the conception for which 
a word stands. Thus, take the word '' hard," or " hard- 
ness," the sphere of the conception includes every ob- 
ject of which we can say "it it is hard." 

47. The Matter or Intension of a conception is the 
Matter. Humbcr of propcrtics which may be ascribed to 
the subject or substance of which we have a concep- 
tion. Thus with the subject "Iron," the matter of the 
conception is " hardness^'^ " dtcctility,^^ " malleahility,^^ 
&c., including whatever may be predicated of iron. 

48. Or to take the conception "man," the sphere 
includes Caesar, Cicero, Washington, &c.,&c., every indi- 
vidual of whom we can say that "he is [or was] a 
man ; " the matter of the conception is " hi7na7ioi(Sy^^ 
" hiped^^^ " rational^'^ " religious^'^ " account ahle^'^ &c., 
including every thing that can be predicated of man, 
whether as a physical, or an intellectual, or a moral 
being. 



I.] OF TERMS. — SECT. II. 16 

49. A distinction is sometimes made in speaking ot 
conceptions between being contained in a contained in 
conception and being contained under it. ^^er^'T^con'! 
The Matter is said to be contained in the con- caption. 
ception ; thus rational is contained in the conception 
" man." But Caesar, Washington, Bonaparte, Frank- 
lin, &c., are said to be contained under the conception 
" man." 

50. The Matter of a conception limits and deter- 
mines the sphere ; thus we include in the The Matter a- 
conception or class "man," every individual n^its the sphere. 
who has the properties of a man. 

51. Conceptions of the same object formed from dif- 
ferent points of view, are called Alternate Alternate con- 
Conceptions, Hence Alternate Conceptions ^^ptions. 
each denote the same sphere by different matter, and 
constitute different names for the same object. Thus 
" height " and " depth " are Alternate Conceptions of 
distg-nce, perpendicular to the horizon, viewed from 
different points. Almost every object m Nature has 
several names, according as it is viewed in one or an- 
other of the relations which it sustains. Thus a Natu- 
ralist would speak of certain animals as " sheep " 
simply ; the Farmer, with reference to his farm, would 
call them '^stoch;^^ and the Commissary, with refer- 
ence to their use as a supply for the army, would call 
them " provisions^ 

52. The cognition of the sphere and the matter of a 
conception are not usually simultaneous acts. 

T r\ ^ n , , • / • 1 1 • . The Matter 

In the nrst perception oi a sing-le obiect, we acquired before 

i. xl- 1,^ V '^ ^' \. the Sphere. 

get the sphere oi its conception, by means 
of some of its most obvious properties ; we acquire the 
others, one after another. In the question, " what is 
that f " '' that " refers to the sphere of the conception 
which we already have in our minds ; and " what "^ to 
the matter which we have not and wish to acquire. 
The same thing occurs in efforts at recollection. We 
remember that something happened, was said or done, 
without remembering what it was ; we have the sphere 



16 LOGIC. — PART I. [chap. 

of its conception in our memory, but the matter has for 
the most part escaped us. 

53. The questions "who" and "what," are an- 
swered by the matter of a conception, which enables 

Questions who? "^^s to determine the sphere. But the ques- 
what? and which? ^{^^ " which," is auswcrcd by the sphere 
of the conception, — which enables us to study out the 
matter for ourselves. 

54. But in regard to the conception of a class, we 
get the matter of the conception before the sphere, 
since it is the matter which determines and limits the 
sphere. 

55. Among the properties or attributes of an object 
of thought, we distinguish some that are inseparable 
from it, as extension and divisibility from matter ; and 
in a man his complexion, his features, his stature, &c. ; 
and other properties which are separable or different, 
at different times and in different places, as sickness 
and health ; his posture, as sitting, standing, or "talk- 
ing, &c. Properties of the former kind are said to con- 
Essence and stitute the Essence"^ of an object of thought ; 

Modes. ^Q latter its modes of existence ; thus the 

name of any object always implies all the essence 
of its reality. But if we wish to express its modes 
we must add something to the name, expressive of that 
mode ; thus " George Washington " denotes the man, 
but does not imply any thing of his modes, as sick- 
ness or health, eating or sleeping, commanding an 
army, presiding in his cabinet, or delivering his fare- 
well address. 

56. Most terms, however, denote a substance as 
existing in some particular mode ; and substance and 



* We use the word ^^ Essence''^ in its Logical sense and not its Onto- 
logical, as denoting that which it is in itself, aside from all the changes 
it may undergo, without becoming a different object ; and not that 
which is necessary to its existence as an object in reality. Without 
its Essence, in its ontological sense, an object could not exist at all ; 
but in the Logical sense it might exist as an individual in another 
genus. 



I.] OF TERMS. SECT. II. 17 

mode, in Logic, is somewhat an arbitrary inJITubsSJJfe 
distinction. Strictly speaking, in the onto- ^« a mode. 
logical sense there are but two substances, matter 
^nd spirit ; and most other words denote one or the 
other of these substances existing in some particular 
mode ; thus take the word " c^^V," it denotes matter 
existing in a certain mode. Again, considering " air " 
to bs a substance, and " wind " is a modal term, 
denoting the existence of " air " in a particular state ; 
or if we take ^' wind " for one substantive word, then 
" gale " will be a modal denoting the existence of wind 
in some one of its modes. 

67. When any property, or a number of them, are 
considered as constituting several objects of thought, 
to which they belong, a class, these properties are 
called Essentia ; thus " man " denotes a Essentia. 
class ; and those properties, without which one would 
not be called a man, are the Essentia of the class ; and 
the class, with reference to these Essentia, Genus, 

is called a Genus. Essentia is the matter of the con- 
ception, and the Genus is its sphere.^ 

58. A word denoting a Genus is called a General 
term. But if the word denote a number of General and coi- 
individuals, not by essential marks belong- ^^^^^^ '^^''^^• 
ing to each of the individuals separately, but rather 
by some mark which belongs to them only as a whole, 
or a body, the word is called a Collective term ; as 
" congress," " church," " army." 

59. From the nature of a general term, whatever 
may be predicated of the term, may be pre- Difference m 
dicated of any individual object included cates. 
under it ; thus if we say, " man is a two-footed being," 

* I do not think so mucli has been made of the distinction between 
the terms which denote the matter, and those which denote the spheres 
of conceptions, as might with profit, in explaining what has been caUed 
the Predicables. Of these, Porphyry, and after him the Scholastics gener- 
ally, have reckoned five: Genus, Species, Differentia, Property and 
Accident ; the two first. Genus and Species, denote spheres, and the 
other three matter of conceptions. 



18 Loaic. — PAET I. [chap. 

we may say of each man, " lie has two feet." But 
this is not true of the collective term ; thus we can 
say of the church, " it is a divine institution," but 
we cannot say of its members, " they are a divine in- 
stitution." 

60. Some words are used only as collective terms, as 
those just mentioned ; while others are sometimes used 

Some words ^^ collcctivc, and at other times as general. 
used in^both Thus if WO Say, ''the Romans conquered 
Carthage," we cannot say that "Cicero con- 
quered Carthage," although he was a Roman. " Ro- 
mans " is here used as a collective term. But if we 
say, the Romans spoke the Latin language, we may 
say of Cicero, he spoke the Latin, for we then use 
" Romans " as a general term. 

61. When we consider any of the properties of 
an object as distinguishing it from a class to which it 
Differentia. docs not bcloug, thosc propcrtics are called 
Differentia, or distinguishing marks. And all the 
individuals which have these marks or properties. 
Species. are called a Species. Thus woolly hair, 
black skin, &c., if considered as distinguishing those 
who have them from other men, are the Diflferentia ; 
and " Negro " is the term denoting the species thus 
distinguished. 

62. Hence the same property may be either Essentia 
or Differentia, just according to the point of view from 

Essentia and which it Is regarded. If we regard black 
th^?'rdation to sklu, wooUy hair, &c., as constituting a class, 
each other. ^|^^j^ Ncgro is a Gcuus, and these properties 
are Essentia. But if we have in mind at the same time^ 
" man," as a higher and more comprehensive class, 
including those who have black skins, woolly hair, &c., 
as well as others which have them not, " man " is the 
genus, and " Negro " is the species. 

63. Hence those properties which are the Differen- 
tia of a class, considered as a species, become Essentia 
when the same class is regarded as a genus, including 
species under it, and vice versa. 



I.] OF TEEMS. SECT. H. 19 

64:, Properties, when regarded as Essentia or Dif- 
ferentia, are considered Essential ; but when properties es- 
not so regarded, are usually spoken of as J|n^^/ '''' ^^''^^ 
Accidental.^ 

65. When any property is considered as distin- 
guishing one individual from another, it has inseparable 
been called Inseparable Accident, Indivi- Occident. 
DUAL Makk or PECuLiARrrY ; and the object thus de- 
noted, is called an iNDIYIDUAL.f individual. 

66. Hence Individuals are included under Species, 
Species under Genera, and so on ; Genus individuals, 

!_• 'J Jxi_i_'i, J Specifis, and 

being considered, the higher and compre- Genera. 
bending sphere, and Species and Individuals, each in 
order, lower and comprehended spheres. 

67. Spheres are said to coincide or be coincident^ 
when they contain some individuals common spheres coin- 
to both; as for instance, "Christian" and pos1t"e. ^° ^" 
" man ; " since all who are included in the sphere 



* Properties tliat belong to an individual, or to the individuals of a 
class only, are said to be peculiar to that individual or class. If a pro- 
perty belongs to all the individuals of the class, it is general in respect 
to the class, or universal. If it belongs to several classes, it is said to 
be common ; a common property. 

Properties, when considered in reference to some end or object, 
for which the thing to which they belong is designed or desired, 
are also called Qualities, or that which qualifies a thing for its lise or 
end. 

f It will appear from the above, that of the five Predicables of Por- 
phyry, two. Genus and Species, must be nouns, as denoting classes ; 
and the other three. Differentia, Property, and Accident, will be adjec- 
tives ; thus, of John Smith, we predicate, as they say, Gemcs, " man ;" 
Species, "Caucasian;" Differentia, "white;" Property, "civilized;" 
Accident, "very short," or "sitting in a chair." 

Genus and Species are said to predicate "m Quid;" Differentia, 
"m Qualequid ;" Property and Accident, "m Quale.^^ 

"Genus," says Aldrich, "is that which is predicated of many, as 
their material or common part, as " animal." — Differentia, that which 
is their formal part, as " rational." — Property, that which is joined 
with the essence, as "risible;" — and Accident, that which is con- 
tingently joined to the essence, as "white," "black," "to sit." But 
in this account of terms, he regards Essentia and Differentia as one, or 
the Differentia as the Essentia (see Aldrich, Oxford ed. 1849, p 20, and 
the notes). 



20 LOGIC. PART I. [chap. 

denoted by " Christian," are in the sphere " man " also ; 
since " Christians are men." 

68. But if two spheres have no individual com- 
mon to both, they are called contrary or opposite 
spheres ; as " dog " and " man," " Christian " and 
" Mahometan." 

Contrary or opposite spheres, however, although 
they may have no individual contained under them com- 
mon to both, may, nevertheless, have matter contained 
Analogous ^^ them iu common. Thus any two species 
Spheres. Comprehended under the same genus, must 

be contrary spheres ; as black or white, as properties 
of men, so that no object can be in both at the same 
time ; yet black and white may be both species of men, 
in which the essentia of humanity is common to all the 
individuals in both species. Such spheres are called 
Analogous. 

69. That genus which can never be comprehended 
summum nudcr a higher genus, is called the summum 

Genus. Qp maximum genus. That species which 

can never comprehend one below it, is called the 

.infima spe- i'f^fima specics. All others are called sub- 
*^^®^' alternate species and genera. The genus, 

however, which is next above any two or more c6- 

proximate Ordinate species is called, in reference to 
Genus. thosc spccics, thc joroximate genus / as 

" man '^ is the proximate genus to " Negro " and 
" Mongol." 

70. Those properties which indicate only the dif- 
separabie fcrcut modcs of the same individual, are 

Accidents. called Separable Accidents ; as sickness or 
health in man, sharp or dull in a knife. 

71. When attributes are common to all the indivi- 
duals of two or more species, they are called Indif- 
indifferentia. FERENTiA, Or poiuts of indifference / or even 
sometimes " common properties," as to have hoofs is 
common to the horse, the ox, the goat, the slieep, &c. 
Hence the having hoofs is the point of indifterence to 
those several species, and may become the Essentia of a 



I.] OF TERMS. SECT. HI. 21 

proximate genus, under which all hoofed animals shall 
be comprehended. 

72. Hence the Differentia is essential to the species, 
and the peculiarities or inseparable accidents are essen- 
tial to the individual. 

73. The matter of a term, used as a general term, 
is the Essentia of the Genus; the matter The Matter of 
of a term, used as a specific term, or to General Terms. 
denote a species, is the Essentia of the Proximate Ge- 
nus (and of course, therefore, of all higher of specific 
and comprehending genera), plus the Differ- '^®™*^- 
entia of that species. And the matter of an individual 
term is the Essentia, plus the Differentia, of individual 
plus the Inseparable Accidents or individual '^®""^- 
properties. 

74. Besides this matter, however, every class must 
have some properties which are not considered as either 
Essentia or Differentia, and each individual 

must have some separable accidents, which Matter "of 
are not necessarily included in the concep- 
tion of the individual. Thus, in forming a conception 
of a man, it is not necessary that we should include in 
the conception any particular posture, style of dress, 
state of health, &c., although he cannot exist except in 
some posture, state of health, &c. 



SECTION IIL 

Of the Whole and its Parts. 

75. The sphere of any conception is regarded as a 
whole. But there are three ways of consid- wholes, of 
ering wholes ; that is, there may be three ^^'^^ ^'"'^^• 
alternate conceptions of the same whole, which we call 
Logical^ Continuous^ and Collective wholes. The esti- 
mate of a whole is called Quantity; the process of 
resolving the whole into parts, is called Division, 



9Si LOGIC. PAKT I. [chap. 



1. Of Quantity. 

76. As there are three alternate conceptions of any 
whole, so there are three ways of estimating the amount 

Quantity, of ^^ that wholc, or three kinds of Quantity ; 
three kinds. Zogicalj Contiuuous^ and Discrete. 

77. Logical Quantity is that which estimates the 
comparative size of the sphere of conceptions, as mea- 

Logicaiauan- surcd by the individuals included under 
*'^y- them ; thus a species is always less than its 

proximate genus, and so on. 

78. In Continuous Quantity the object of thought 
is always considered simply as a reality ; thus a point, 

Continuous ^ lii^^? ^ surfacc, a triangle, a circle, &c., are 
Quantity. considcrcd as continuous quantity. Theo- 
rems which are demonstrated concerning them in Geo- 
metry and Trigonometry, have no connection with the 
length of the lines, or the amount of the area that may 
be inclosed by them. 

79. So also the properties which may be predicated 
of substances in different degrees of intensity, are con- 
sidered as continuous quantity. 

80. Discrete Quantity contemplates a whole as a 
union or accumulation of parts. These parts may be 
Discrete Quan- uucqual, and cach have a differentia of its 
^*y- own. Or they may be equal and have no 
distinguishing marks. In that case they are merely 
units, and quantity is mere number ; — the science of 
this kind of quantity is Arithmetic. 

81. In Continuous Quantity, the whole is not con- 
continuous ccivcd as made up of parts, or divisible into 

wholes not made , .-, ^ c •/ i i 

up of parts. parts ; though oi course it may be so made 
up, and consequently divisible. 

82. In Discrete Quantity we have such terms as the 
cardinal numbers, fractional expressions. Nothing, or 

Terms and zcro, dcuotcs uot auv Quantitv, but the ab- 

Limits in Dis- ' r* ,» , ./J- ^^ •/ -'. , 

Crete Quantity, scucc 01 quantity or quantiiicatioii ; ana the 
last expression, in discrete quantity, is the indefinite / 



I.] OF TERMS. SECT. HI. 23 

a sum so large that it cannot be expressed, the limit 
cannot be pointed out, but not so lar^e that it may 
not be increased by addition and dimmished by sub- 
traction. 

83. In Continuous Quantity we have such terms as 
denote indivisible objects of thous:ht : any 

-....p.-i *^ ,. Ji.' Limits in Con- 

object m lact whose conception does not im- tinuous Quan- 
ply a union of parts. And besides names ^'^' 
denoting such objects of thought, we have also the 
positive, the comparative, and the superlative forms of 
adjectives denoting degrees of intensity; and the last 
expression of continuous quantity is " injinite^^ and it 
implies that of which extension cannot be predicated.* 

84. Logical Quantity begins with the individual, 
and takes note of the higher classifications. Limits in Lo- 
up to its last term, the Absolute,— iheit which ^^^^* Quantity. 
includes all being, which is genus without ever being 
species, the summum genus. 

85. Discrete Quantity is applied to the objects 
which are included in the terms of the other Application of 
kinds of quantity ; thus a line, or angle, are Sy^'to^^ Logical 
continuous quantities. But when we say the ^nd continuous. 
line has so many feet, or the angle is of so many de- 
grees, we apply discrete quantity to the measurement 

* Even space and time form no exceptions to this remark : for nei- 
ther time nor space, strictly speaking, are extended. We have simply 
a conception of extension, as applied to something in space or in time, 
but not to space and time themselves. 

Among the many classifications of properties, we have one that is 
useful for many purposes — into primary and secondary ; of which the 
primary can be predicated of substances only, — the secondary not of 
substances at all, but only of their primary properties ; thus, extension 
is a primary property of matter, length is a secondary property — a 
property of the extension of a body. When we say a body is so long, 
we mean that its extension or extent is so long. " Thinking " is a pri- 
mary property of mind; "intense," "close," &c., are proper: ies of 
" thinking." 

Now, "infinite" and " extension," are incompatible properties; 
both primary ; and can neither of them be predicated of the other, nor 
in fact of the same substances. We say space is infinite, and we have 
extension in space. We say GOD is infinite, but we never speak of 
His extension. 



24 LOGIC. — PAKT I. [chap. 

of objects of continuous quantity. In like manner, when 
we attempt to number the individuals comprehended 
in the sphere of any logical whole, whether species or 
genus, it must be done in terms of discrete quantity ; 
thus the discrete quantity of the sphere " man " is 
800,000,000 ; that is the whole number of men on the 
earth. 

86. But by far the greatest part of the properties 
of substances, considered as continuous quantity, can- 
Not aii objects ^c)t be measured by discrete quantity; thus 

auaS?t"y'^n°bl ^c cauuot measure in any such way the in- 
80 measured, tcusity of color, of tastc, of smcll, of density, 
&c., among the properties of material substances ; nor 
that of virtue, wisdom, courage, &c., among the pro- 
perties or attributes of mind. We may be able to 
distinguish a greater or a less intensity — that is, a 
more and a less — but how muck greater or less is 
what we have no means of measuring or express- 
ing. 

2. Of Division. 

87. That process by which a Whole is resolved into 
its Parts is called Division ; and, as there are three 

Division of kinds of Quantity, so there are three kinds 
three kinds, ^f Divisiou \ Physicol^ Mathematical or iV^ 
merical^ and Logical. 

88. Physical Division divides continuous quantity ; 
thus we divide a loaf of bread into pieces. Now these 
Physical. parts are hread — that is, have the essentia of 
the whole, but they have no. proper differentia of their 
own constituting them different species of bread — as 
" wheaten bread," " barley bread," &c., but they are 
considered still as parts, and are conceived of in rela- 
tion to the whole. 

89. Numerical Division divides a discrete quantity 
or number into parts, each of which is considered as 
Numerical. a uuit or factor in reference to that whole. 
Thus we divide a foot into twelve inches, a yard into 



I.] OF TERMS. SECT. HI. 25 

three feet, &c., and the collective whole with Dividend, 
reference to Mathematical Division is called Dividp:nd. 

90. Logical Division divides the sphere of the 
Genus or Logical Whole into species, each Logical. 
having the Essentia of the whole and a Differentia 
of its own, belonging to each individual contained 
under it; and into individuals, each having individual 
marks or inseparable accidents of its own. Logical 
Division is called Classification. cihssification. 

91. Thus physically we should divide a man into 
head, trunk, and extremities — or into bones, illustration of 
muscles, tendons, membranes, fluids, &c. ^^i^is^^n- 
Mathematically w^e should divide the race into com- 
panies of tens, or fifties, or thousands, as the case might 
be. Logically we should divide them into Mongol, 
Caucasian, and Negroes ; or into Pagans, Mahometans, 
Jews, and Christians ; or into civilized, barbarous, and 
savage, &c. 

92. The number of individuals included in any con- 
ception or logical whole may be divided in 

several different ways. Thus the inhabit- sion7^'of !he 
ants of the Earth may be divided ethically 
into Caucasians, Mongols, Negroes ; or politically into 
English, French, Spanish, Russians, Chinese, &c. ; or 
in reference to their religion into Christians, Jews, 
Mahometans, Buddhists, &c. 

93. That which determines us to any one of these 
several divisions of which any logical whole pivisive Prin- 
is susceptible, is called the Divisive Prin- ^^'p^^- 
ciple or the Principle of Division, As in the example 

gLst given. Race, Polity, and Religion ^re the Divisive 
rinciples by means of which the divisions are effected. 
In mathematical division the divisive principle is called 
the Divisor, 

94. The divisions of the same w^hole effected by 
the different Principles are called the Co- coordinate Di- 

-r-\. . . -*■ visions. 

ORDINATE Divisions. 

95. The several parts into which any whole may 
be divided by means of the same Principle of division 

2 



26 LOGIC. — PAKT I. [chap. 

are called Coordinate parts, and the terms denoting 
Coordinate them are CooKDiNATE TERMS, as Christians, 
Parts. Jews, and Mahometans, &c. 

96. The Coordinate parts of a numerical Division 
Factors, Species, are callcd Factm's — with reference to the 
divided whole, or Dividend. In Logical Division, the 
Whole is called a Genus, and the Coordinate parts are 
Sjpecies. 

97. But the parts of two coordinate divisions of the 
Disparate parts, samc wholc are Called Disparate parts ; and 
the terms denoting them Disparate terms in reference 
to each other — as Caucasians, Russians, and Maho- 
metans. 

98. Any one of these parts however may be as- 
sumed as a whole, and divided as though it were not 

Parts assumed includcd iu a higher and morc comprehen- 
as wholes. gjy^ wholc, and so on, until the sphere of the 
conception comes to be an individual. 

99. But when any whole is divided into coordinate 
parts, and these coordinate parts are again subdivided. 

Subordinate thcsc divislous with reference to the first 
Divisions. division are called Subordinate, and the 
parts of these subordinate divisions are called Subor- 
dinate parts. 

Thus let X be divided by coordinate divisions, and 
Illustrations, ou different principles of division, as follows : 

1st. 2d. 3d. 

X into X into X into 

A, B and C, D, E and F, G, H and I, 

2^i8t. ]j2d. ^3d. ^j.^ coordinate divisions. 

A, B and C are coordinate parts in relation to each 
other, so also are D, E and F, and likewise G, H and I. 
But A, D and G, or B and F, or E and G, &c., are 
disparate to each other. 

Let now A, B and C be subdivided, 

A into B into and C into 

a^ 5, and c, d^ e^f^ g^ A, L 

These are subordinate divisions. 



I.] OF TEEMS. SECT. IH. 27 

a^ 5, ^, d^ e^f^ g^ h and i are all subordinate parts 
to X^«*- 

But a^ h and c^ &c., are coordinate to each other, 
and a^ d^ g^ &c., are disparate to each other, as in the 
first division the. parts occupying similar places were 
disparate. 

100. Any conception including in its sphere more 
than one individual, though it may denote 

but a coordinate or a subordinate part in tio1i"Lay''b?^; 
reference to another and more comprehen- 
sive whole, may become nevertheless a logical ^vhole 
or unity itself with coordinates and subordinates under 
it. And each term or conception, whether whole, co- 
ordinate or subordinate, and in whatever degree of 
subordination, until we come to a term that' denotes 
but one individual, will have a sphere and a matter of 
its own, and so be capable of a logical division. 

101. As we have said, the parts in any Logical 
Division are called Species, And besides the Alternate parts 
Coordinate, Disparate, and Subordinate Spe- ^r species. 
cies just described, we have in Logical Division Alter- 
nate Species also. These are species the Differentia 
of which is a part of the matter of Alternate concep- 
tions of the same object. Thus statesman and philoso- 
pher may be Alternate conceptions of the same indivi- 
duals, so that the same men may be both statesmen and 
philosophers, though of course an individual may be 
one without being the other. In this view of the mat- 
ter statesmen and philosophers are said to be Alternate 
Species. 

102. The last element of a Logical Division is called 
individual. But the individual may be either Absolute m- 
Absolute or Relative. It is absolute wdien it '^i^i^^ai''- 
can be divided no farther. Thus the mind is an abso- 
lute individual ; the chemical simples such as iron, 
sulphur, sodium, &c., are also absolute individuals, 
because they cannot be resolved or analyzed into any 
component elements. 

103. On the other hand, most of the objects of 



28 LOGIC. PART I. [chap. 

thought are merely relative or assumed individuals ; 
Relative In- that is, thej are individual only in reference 
dividiiais. |.Q ^i^Q purposes for which they are at the 
time before the mind. In this view " man " is an 
individual, in reference to any classification of the 
animal kingdom. But in reference to a classification 
of substances as spiritual and material, man is not an 
individual — his mind belongs to one class and his body 
to another. So with reference to a Treatise on Materia 
Medica, carbonate of soda, for instance, is an indi- 
vidual ; but in reference to chemical analysis it is a 
compound, resolvable into carbonic acid and sodium. 

104. The following are regarded as the fundamental 
vfston"' ""^ ^'' Canons of Division. 

(1.) the coordinate parts must contain all that was 
contained in the whole, and nothing that was not con- 
tained in it. 

(2.) Each coordinate part must have a narrower 
sphere or be smaller than the divided whole. 

(3.) No unit or individual can be contained in more 
than one coordinate part. 

Thus if one should divide his library into the co- 
Exampies. Ordinate division, folios, quartos, octavos, &c., 
and Greek, Latin, English, French, German, &c., and into 
philosophy, history, physics, mathematics, poetry, &c., 
each division would be good. But if he should divide 
into folios, octavos, Greek, history, philosophy, &c., the 
division would be faulty. It would not be made on 
any one principle of division, and the same book might 
be included in several of the parts. 

105. The division of a Logical Whole into Alternate 
Species is only an imperfect division, and does not 

fulfil the conditions as above specified. It 
cies^'"'^vioiSte rcsults tVom the very nature of Alternate 

conceptions, that they may be all of them 
predicated of the same object ; since they are but 
Alternate conceptions or difterent views of that objec*. 
Hence if they are taken as the Differentia of Species, 
the same individual may be in more than one of them 



I.] OF TERMS. SECT. IV. 29 

at once ; thus a man may be a Christian, a gentleman, 
and a scholar, all at the same time. Still, 
however, the Alternate Species must include aif the in°divid" 
all the individuals comprehended under the 
Logical Whole or Proximate Genus. If we divide the 
writers of a nation, for instance, into poets and prose 
writers, the same writer may belong to both species ; 
but there must be no one who does not belong to one or 
the other of them. 

SECTIOiSr TV. 
The relation of Cause and Effect. 

106. When any object of thought is considered in 
relation to that which brought it into exist- qause and 
ence, or as having had a beginning, it is ^^''^^'• 
conceived of as an Effect ; and when an object is con- 
ceived in reference to what it may bring into existence, 
it is conceived of as a Cause. 

107. Nearly every object of thought is conceived 
as both Cause and Effect ; — Effect in refer- ^very object 
ence to something which has preceded it as a SerL^'s^^cau^e 
condition of its existence ; and as Cause in °^ ^^^^'• 
reference to something which follows it or whose exist- 
ence is either occasioned or conditioned by it. 

108. Thus starting from any object of thought con- 
ceived as effect, we may direct our thoughts cause auso- 
to its cause, and from that cause conceived ^"^^• 

as effect, to its cause, and so on until we come to the 
First Cause or Cause Absolute. So it is that whatever 
we know by its own properties directly we always 
know and conceive of as effect ; and the mind of neces- 
sity refers to something else as the ground and cause 
of its being. But when we come at last to that Being 
whom no man hath seen or can see, and whom we 
know only through the manifestation of His wisdom, 
and power, and goodness — through the effects of these 
transcendent attributes. Him we know only as Cause. 
He is not only the Cause and Creator of all things 



30 LOGIC. PART I. [chap. 

visible and invisible, but He is also the Cause as Au- 
thor of the Revelation which He has made. Hence we 
know Him only through His works and His Word, 
and the mind refuses to conceive of Him as an Effect. 

109. But with this only Exception, cause and effect 
Cause and Ef- arc but alternate conceptions of the same ob- 

conceptioliT ^ ject of thought. Each object of thought is 
susceptible of both conceptions, and each in turn de- 
mands both. In this view all objects of thought, con- 
sidered as causes, are distinguished inro Absolute and 
Selative — the One only being Absolute, all others 
being relative. 

110. Again we conceive of Mind as a cause in a 
different sense from what matter can be. Motion, in 
oause Primary matter, always refers the mind to something 

and Secondary. ^^^ ^f ^^ moviug mass, as its causc — this 
cause we call a Force. But if we see a being possess- 
ing mind, in motion, we are content to consider him- 
self as the cause of his own motion ; and reason is 
satisfied when we refer to his will as the cause of the 
movement. Hence we distinguish between Primary 
and Second causes, and call those Primary which are 
sufficient causes — and those Secondary which only refer 
us to something else as the cause of its acting, as cause ; 
and so on until we come to intelligent moral Agency, 
as the only Primary Causes. 

111. Besides the above distinctions there are seve- 
ral other senses in which the word Cause is used, or in 
which the object of one conception may be regarded 
as the cause of the object of another. 

(1.) The Efficient Cause is that from which emanates 
Efficient Cause, the forcc that produccs the Effect. 

(2.) The Occasional or Exciting Cause is that which 
Occasional. puts thc Efficient Cause in operation, as the 
spark in the explosion of gunpowder. 

(3.) The Material Cause is the matter or Essentia 
Material. of wliicli any tiling consists."^ 

* As the Essentia of any class considered as a Genus is the Material 
of that Ginus, the Essentia may be called with reference to this fact 
the Ma'rrial Properties. 



I.] OF TERMS. — SECT. IV. 31 

(4.) The Formal Cause is that which determines 
the specific mode of the existence.* Formal. 

(5.) The Final Cause is that for which a»iy thing 
exists or is done ; and, " Final 

(6.) We have also what are called Negative Causes, 
as when we say " the want of rain caused Negative. 
a severe drought," — '' the absence of heat," or which 
is the same thing, " cold congeals the river." 

112. Of the six kinds of Cause just enumerated, the 
1st and 2d, the Efficient and Occasional, common Names 
are usually spoken of as Causes; and much o^^^^m. 
confusion often arises from not distinguishing between 
them. The Material Cause is usually spoken of not as 
a cause but as " the nature of the thing ; " the Formal 
Cause as its " characteristic ; " and the Final Cause as 
its "design" or "object." 

113. Thus if we take an act of virtue, the person 
who performed it is the Efficient Cause ; illustrations. 
the motion which induced him to do it is the Occa- 
sional Cause ; the fact of its being a free act and not 
one of necessity, or even instinct, is the Material Cause ; 
the nature of the act, its conformity to right rules of 
action is its Formal Cause or characteristic, and makes 
it a virtue and not a vice ; and the object for which it 
was done is its Final Cause. 

114. Causes are sometimes considered as Transient^ 
Permanent^ or Immanent. 

A Transient Cause is one which passes away after 
its efficiency has been exerted. Thus occa- Transient cause, 
sional causes are for the most part transient, as the 
spark that ignites the powder. A Perma- permanent cause, 
nent Cause is one that remains, and from which the 
effect is continually flowing — as the sun and the lamp 
are permanent causes of light. An Imma- immanent cause, 
nent Cause is one that remains in its effect ; the Mate- 
rial and Formal Causes are always Immanent. 

* As the Differentia of Species are the Formal Cause of the Species, 
with reference to this fact they may be called for the sake of con- 
venience the Formal Properties. 



32 LOGIC. PAKT I. [chap. 

115. Causes with reference to the fact that they 
^ Called Ante- alwajs cxist bcfore the Effect, are sometimes 
conTequents^li callcd Antccedents merely. So also Effects 
for the same reason are soilietimes called Consequents 
or Consequences merely. 

116. Effects are either Immediate or Remote. The 
Immediate Ef- Imm^ecUate effect is that which follows at 
Remote. oncc ; tlic Rcmotc effects or consequences 

are those which appear afterwards, but not until after 
an interval in which they are not seen. 

117. Again, Effects or Consequences are Direct 
and Accidental, Direct when necessarily following 

Direct. Acci- froui thc activity of the Cause, and always 
dental. implied in the conception of its agency. 

But those effects which are not invariable attendants 
upon the activity of the Cause, and are not considered 
as ]iecessarily implied in it, or as necessary to its ade- 
quate conception as a cause, are called Accidental / 

Undesigned, and iu refereucc to an intelligent cause they 
are called Undesigned. 

SECTION V. 
Of Difference^ Identity^ Resemblance and Analogy. 
Difference is of two kinds — (1) in kind, and (2) in 

Difference of rlarvvoa 

two kinds. aegiee. 

118. Although any common name may be used as 
genus, yet there are certain obvious and natural pro- 
Difference in perties of all objects of cognition, by which 

^'"'^- they are referred to natural classes. In this 

classification these more obvious properties are assumed 
as the basis of the classification. When therefore two 
objects do not agree in possessing each the same pro- 
perty in this natural classification, they are said to 
differ in kind. 

119. But when two objects of cognition are con- 
ceived as belonging to the same natural genus, and are 
In Degree. comparcd ouly with reference to some one 
property or class of properties which they have in 



I.] OF TERMS. SECT. VI. 33 

common, tliey are said to differ in degree only. In this 
case the objects possess — the one more and the other 
less of — the property or properties which are made the 
basis of the comparison. They differ only in the degree 
or intensity in which they possess the property com- 
mon to both, and in reference to which they are com 
pared. 

120. When the difference is only in separable acci- 
dents then it is said to be " identity, "^^ It is identity, 
the same individual under different circumstances or 
at different times ; thus '' sick " or '' well," " sitting " 
or ''walking," ''sleeping" or "waking," with re- 
gard to a man ; "hot" or "cold," "round" or "irre- 
gular," " bright " or " rusty," &c., of a piece of metal, 
are mere separable accidents denoting different states 
or modes of the same individual substance. 

121. The properties common to any two or more 
individuals conceived as belonging to the same species, 
constitute what is called Similarity or Be- similarity and 
semhUmce. And the properties which are contrariety. 
different in any two or more individuals conceived as 
belonging to the same species, constitute Contrariety. 

122. Hence similarity and contrariety are between 
individuals conceived as belonging to the same species. 
Or these terms may be applied in the same w^ay to 
species conceived as comprehended within the same 
proximate genus. 

123. The properties in common between individuals 
conceived as belonging to opposite or differ- Analogy, 
ent species constitute what is called Analogy. 

SECTIO]^ VT. 

Of Definition and Description, 

Before proceeding to explain more fully the terms 
which will be of frequent use throughout this Treatise, 
it may be well to say what we mean by a Definition, 
and what by a Description ; reserving the fuller dis- 
cussion of the subject to the chapter on Method. 

2^ 



L 



34 LOGIC. PART I. [chap. 

124. A Definition is any Proposition in which the 
Definition. word or thing defined is the subject, and 
the predicate gives us the matter of its conception. 

125. A Description is any Proposition which indi- 
Description. catcs the sphcrc of a conception, either by 
enumerating its parts or pointing to the place in which 
or the time where it may be found. 

SECTION VIL 

Of the Quality of Terms. 

126. The Quality of a Term indicates the manner 
Quality of Terms, in which it reprcscnts the conception or 
cognition for which it stands."^ 

* Aristotle divided the categories into ten : Substance, Quantity, 
Quality, Kelation, Place, Time, Position, Possession, Action, Passion, 
(Organ, c. iv.) And he adds (Top. I. c. ix.), "for accident, and genus, 
and property, and definition, [I am not responsible for his divi- 
sion,] will always be in one of these categories, since all propositions 
through them signify either what a thing is, or its quality, or quantity, 
or some other category." Aristotle's illustration is. Substance ^'man" 
Quantity '■^ one^' Quality *^ white,''^ Relation ^'greater,''* where " in the 
Forum^^' when " yesterday,'" Position " sitting" Action *' whatever he 
may he doing," Passion ^^ whatever may he heing done to him" 

Now it is very possible that every thing that can be said of any sub- 
ject may be included in one or another of these categories. The list 
seems to be very complete. But I have been unable to see its utility, 
and therefore I have omitted it. And in that respect it is like mmch 
else in the writings of this Father of Logical Science. 

At a later period Kant gave another list of the categories. Aristotle 
had classified them from the outward properties of things. Kant 
classified them from the ideas determining their cognition — into four, 
each of which contains under it three varieties or dimensions. 

i One. i Real. 

I. Quantity \ Some. II. Quality \ Limited. 

( All. ( Non-Real. 

( Substance, or Property. 
in. Relation -| Cause, or Effect. 

( Action, or Reaction. 

i Possible, or Impossible. 
IV. Modality •< Existence, or Non-Existence. 
( Necessary, or Contingent. 

Tliis list of categories is important rather to Metapliysics than to 
Logic, as determining the conditions and possibility of knowledge rather 



I.] OF TERMS. SECT. VH. 35 

127. We have already had occasion to concrete ana 
explain what we mean by concrete and ab- ^^''*'''; 
stract terms (see 43), by denotative and con- coSnoUuve^"** 
notative (see M), by substantive and modal Mod'S"^""^^"*^ 
(see 55) terms. 

128. A term denoting a class is called general with 
reference to its including more than one in- General Terms, 
dividual, and specific with reference to its specigcTerms. 
distinguishing them from all others. 

We will now proceed to notice a few more of the 
diflferences in the Quality of a Term. 

129. Terms denoting the same conception are called 

Synonymous, Synonynnous. 

130. Terms denoting Analogous Spheres are called 
Analogous Terms. 

131. Terms having the same logical force, though 
not analogous or synonymous, are called EquipoJient. 
Equipollent. 

132. Terms which denote sometimes one conception 
and sometimes another, are called Ambiguous. Ambiguous. 

133. Terms which cannot be predicated of the same 
subject at the same time and in the same respect, are 
called Inconvpatible. Thus " sitting " and incompatible. 
" standing " cannot be predicated of the same man at 
the same time. " Master "^^ and '' servant^^ can be pre- 
dicated of the same subject at the same time, but not 
in the same respect. Thus one may be the servant of 
his superior and master of his dog ; but he is not master 
and servant in respect to the same thing or in the same 
respect. 

134. A PosnivE Term is one which implies the 
reality of that which it denotes. All terms positive. ^ 
therefore denoting genus, species, or individuals, or the 
properties of them, are Positive. 

than the deduction of one thought from another, and the systematic 
construction of those thoughts into knowledge and science. 

In the foUowing Sections, therefore, I have confined myself to such 
classifications of terms as seemed to be useful for the purposes of deduc- 
tion, and omitted all others on the ground that the inclusion of -what- 
ever is not useful is a hinderance. 



36 LOGIC. PART I. [chap. 

135. But the sphere of a positive term is a limited 

The Sphere of Sphere,^ and excludes all that has not the 

um/ted^ ^^^^ Essentia of the conception denoted by the 

Positive ; thus the conception circle excludes from its 

sphere all figures that are not circles. 

136. A Positive sphere therefore necessarily im- 
plies another, in which are included all objects that 

Implies a Ne- ^^ 1^^^ possess the attributes Contained in 
gative Sphere. ^]^^ matter of that conception. The term 
that denotes this sphere is called a Negative Term. 

137. The sphere of the Negative Term is the com- 
Neffative a plemcut of that of its Positive in the sum- 

complement of ^ v i j. i. i. Tx i» xl • 

the Positive, mum gcnus, or absolute totality oi things. 

138. A Privative Term is one which denotes an 
Privative, objcct OT class of objccts in which there is 
an absence of some property, usually considered as 
belonging to the conception of its proximate genus or 
species. 

139. When we speak of the Essentia as that with- 
out which an individual cannot belong to a genus in 
Illustrations, natural classification, we refer rather to the 
conception than to the actuality of the individual. 
Thus one would say that reason is of the Essentia of 
man, and yet we would not say that an idiot was not a 
man. We recognize the idiot as one who is accident- 
ally deprived of that which belongs to the idea or con- 
ception of his species. He is no less a monster, a 
lusus naturcB^ than a horse with reason or a dog that 
could talk. 



* This is so, or Pantheism is inevitable. Infinite is not so much 
without limits as out of limits ; as red is not so much a long color 
as a color out of length ; that is, not included in any Genus of which 
any of the terms denoting extension can be predicated. But if the 
term God does not denote a limited sphere, then of course there is 
nothing which is not God — God is all — or Pantheism. But it is one 
thing to sa}', the term "God" denotes a limited sphere; and to say, 
that God is limited, or not infinite. "Limited" and "infinite" are 
not antithetic or opposites in the same kind, like '^long^^ and '* shorty'* 
''red" and ''yellow,'' but disparates rather, like "long'' and " red^** 
or "short'' and " yellow." 



I.] OF TERMS. SECT. VII. » 87 

140. Thus " idiotic " when predicated of man, or 
''hlind^^ when predicated of an animal, are Privative 
terms. We do not speak of "dumh^^ as predicable 
of a triangle, although it implies the presence of no 
property, but only the absence of one which never 
belongs to a triangle. So with " idiotic " in reference 
to a mountain or a brute even ; Privative though it be, 
it denotes the absence of a Differentia or Property 
which can never be predicated upon the Essentia of 
" angles," of " mountains," or of " brutes." 

141. The Negative, as we have said, is the comple- 
ment of the Positive in the Summum Genus 

or absolute totality of things. But the Priva- piemelus pft™e 
tive is the complement of the Positive in prolimlte" ce^ 
the Proximate Genus only ; as " wise " and 
" idiotic " in reference to men — '' blind " and " see- 
ing" in reference to '' animals," which thus become 
p?'o hac vice a proximate genus. 

142. Hence it is obvious that Privative terms are 
vastly more frequent than Negatives. In ^^^ ^^^ n^ 
fact there are but few really Negative terms ^^^'"^ '^^'^°'^' 
in use. Which they are can be determined only by the 
usus loquendi of each language, and the peculiarities 
of localities and of the authors who use them ; thus A 
and non-A are a Positive and its Negative. 

143. The distinction between them however is less 
necessary to be made on account of the fol- 
lowing: facts with re2:ard to their use. If the thf Tstlncfion 

, *-* -\ ' i * I * 1* • i between Nega- 

term occurs as a subject, it is oi no import- tives and prwa- 
ance whether it be Negative or Privative ; ^^'^^"®^^'■^^^• 
though not the same they are equipollent in that posi- 
tion. But if the term occur as a Predicate it is of 
no importance for the most part, since the subject itself 
is the sphere of the Proximate Genus, and thus limits 
the individuals which are taken into the scope of the 
judgment, and all individuals comprehended vet the 
sphere of the subject and not included in any position 
used as a Predicate, must be included in its Privative 
as well as its Negative. Thus let " wise" be a positive 



38 • LOGIC. PART I. [chap. 

Predicate, and we say " some men are wise, and 
some men are foolish." It is of no importance whe- 
ther foolish is a ]S"egative .or a Privative term, since in 
either case and alike, it includes all men who are not 
" wise ; " since some men are " wise " and the rest are 
" otherwise." 

SECTIOI^ VIIL 
Of the Quantity of Terms. 

144. Terms expressive of Discrete Quantity are 
either Nunfierals or Ordinals, The Numerals denote 

Numerals and ^hc uumbcr of uuits, as " three ^^^ "four^^^ 
Ordinals. "five / " aud thc Ordinals the order in which 

any particular unit stands with reference to the other 
units in any given series, as " third^^^ "fourth^ " sixthP 

145. Terms expressive of Discrete Quantity are also 
divided into such as express units merely, as " one^'* 

Units, Tens, " two^^ " three^'' &c. ; such as express tens of 
andHulidreds.' ^^j^-g^ ^s '' ten^^ " twenty^^' "thirty^'''' &c. ; 
and such as express hundreds, as " one hundred^'^ 
" two hundred^^ &c. This classification of the terms 
in Discrete Quantity is of great service in discussing 
the elementary Methods of the science of Numbers. 

146. We have also other classifications, as " odd " 
and " even^'' " roots^'^ " squares^'^ " cvhes^'^ " surds^^ 

^' rationals^'^ &c. But as we shall not go 

Roots! powe^; into the discussion of the Logic of Discrete 

' *^ Quantity — far enough to require the use of 

these terms — it will be unnecessary to discuss them at 

length. 

147. Then we have such terms as " Positive " and 
'^ Negative^'' which have been already considered in 

Positive and the preceding sections. As expressions of 
pfscrete^auaii" Discrctc Quautitv they have relation to 
tity. • u 2ero " or " nothing^ They indicate the 

distance above and below that starting point — the one 
showing the number of units above or more than 
nothing, and the other the number below or less. 



I.] OF TERMS. SECT. VIH. 39 

148. The word " infinite " when used in discussions 
of Discrete Quantity, indicates either the absence of 
Quantity altogether, or that the object of 
thought is out of the sphere of Discrete pi^cUe^alfan" 
Quantity altogether. That which is inji- ^'^^' 
nitely small is Nothing ; and that which is infinitely 
large is something with which the terms of Discrete 
Quantity are incompatible. Thus if we divide nothing 
by two I, the answer or quotient is said to be infinitely 
small ; that is, there is none. If we divide two by 
nothing |, the quotient is said to be infinitely large or 
infinite. But there is no quotient at all. There is no 
division in either of the above cases, for the obvious 
reason that we cannot divide without both a divisor and 
something to be divided. In each case therefore we 
perform no operation and get no results in Discrete 
Quantity. ' " Small " and '' large " imply Continuous 
Quantity ; but when they become infinite, they are 
beyond the reach of Discrete Quantity. This is shown 
also by the fact that they never occur in the process 
of a calculation, but only are results at the close of the 
process. 

149. In Continuous Quantity " Positive " is a 
term which denotes the reality of Quantity, positive and 
and '' JSTegative^'^ is a term which denotes cSnuois 
its absence ; the same in relation to Con- Q-uantity. 
tinuous Quantity, as " Infinite " does in relation to 
Discrete Quantity. 

150. Then we have ''Comparatives^^ and ''Super- 
latives^ and these too in opposite directions p^^.^^^^ ^^^ 
from the Positive ; thus let us take " wise" paratiyes,' and 

. ,. , ^ T T ,f Superlatives. 

as a positive term, and we nave " w.ore 
wise," and " less wise," as Comparatives of opposite m. 
opposite intensity \ and " most wise," and ^^"'•^^• 
" least wise, " as Superlatives of opposite intensi- 
ties. 

151. In Logical Quantity we have but two varieties 
of terms to be noticed. 

152. Any term denoting a Logical Whole, whether 



4:0 LOGIC. — PART I. [chap. 

Individual, Species, or Genus, is called a Distributed 
Distributed and term. And any term denoting any unde- 
undistributed. tcrmiucd part of such a whole is called an 
Undistributed term. 

153. All individual terms are therefore always and 
necessarily Distributed. Any term denoting genus or 

species, standino; alone and sin2:ly, or used 

Terms with- ^ ,i ' "u • ^ ^ i? X> ., . ^ '^' . 

out a sign are as the suDject 01 a proposition, is always 
taken as Distributed, or in its broadest sense, 
unless the contrary is indicated by some word or words 
limiting its comprehension, as " so'ine men," " mmiy 
books," ''few wise men." 

154. We are to notice, however, that any words 
which give the Differentia of an included species, 

Specific terms constitutc thereby a specific and not an un- 
are distributed, distributed tcrm. As in the cases just given, 
" some men" does not indicate what part or how many 
of the race of men we intend to speak of. " Many " im- 
plies a larger part than " few " ordinarily, but neither 
of them enable us to distinguish the individuals in- 
tended, from the others included in the same general 
term. But if we say " wise men," " religious books," 
the adjectives " wise"^^ and ''religious^'' give differ- 
entia of species, comprehended under the genera 
'' man^^ and ''hoolis ;^^ and the specific term "wise 
men " is as completely a distributed term as the generic 
"men" itself — "some wise men" would be undis- 
tributed of the specific term. 

SECTIOIS' IX. 

Of the Oj>jposition of Terms. 

155. Among the properties of substances we per- 
ceive some which always imply others. Thus length as 

Opposition of ^ propertj^ of matter always implies breadth. 
Terms. g^^ ^]^^^ wliatcvcr lias the one must have the 

other. (A line can hardly be said to have length ; it 
rather is length.) A beginning always implies an end, 
extension always implies divisibility, &c. 



I.] OF TERMS. SECT. IX. 41 

156. The relation of such properties is called a 
Belative Ojoposition^ and may be of two Relative op- 
kinds. position. 

(1.) Where the correlative properties inhere in the 
same substance, as "length" and ''breadth," ,„ ^^^ ,^^^ 
"beginning" and "end," " extension " and 8ut>3tance. 
" divisibility," &c. 

(2.) Where they necessarily imply different sub- 
stances, as "parent" and "child," "sub- ^ different 
ject" and "ruler;" and the two terms ^^*''^°^^^- 
taken together are called Correlates. 

157. Again there are certain properties which im 
ply the absence of certain others ; this relation consti- 
tutes Contrary Opposition, as "vice" and contrary 
"virtue," '^ white" and "black," "hot" Terms, 
and " cold." In fact the differentia of coordinate spe 
cies are always contraries to each other. Contrary 
terms are called Antithetic in relation to Antithetic 
each other. 

158. There are properties also which may coexist 
in the same substance, yet in such a way that the more 
of the one the less of the other — these are called 
Sub-contraries, Thus " bitter " and " sweet " sub-contraries. 
are words which denote two sub-contrary sj)heres, since 
whatever object is the one is capable of being the 
other. The same object may be both at the same 
time, that is " bitter-sweet," and the more of the one 
the less of the other. Beauty and Utility are two 
more such sub-contrary spheres, since the same object 
may be both beautiful and useful, and for the most 
part that which is the most of the one is the least of 
the other. 

159. In the case of both Correlative and Antithetic 
terms the one always implies the other, thougli in dif- 
ferent ways, and in both cases also one of the pair can 
never be fully understood without the other. 

160. When terms are opposite, botii in Quality and 
Quantity, they are said to be in a Contradic- contradictory 
TORY Opposition. Thus aiiv Positive term '^^^^- 



4:2 LOGIC. PAET I. [chap. 

and its undistributed Negative have a Contradictory 
Opposition, as " men," and " some not-men ; " or " some 
men," and " all not-men." 

161. From the foregoing discussions the following 
inferences may be drawn, which it will be useful to 
remember. 

(1.) Of any term as subject the specific term next 
above it, as animal to man, or its matter, may be predi- 
cated, and so on through the subaltern genera and 
species up to the summum genus. 

(2.) Of correlative terms : 

(a) If they are correlated in the same subject, if 
one is predicated of a subject the other must be 
also. 

(h) If they are correlatives in opposition subjects, 
the other cannot be. 

(3.) Of sub-contraries^ both may be predicated of 
the same subject. 

(4.) Of contraries, both cannot be predicated of the 
same subject. 

(5.) Of contradictories, if one is not predicable of a 
subject the other must be. 



nj OF PROPOSITIONS, — SECT. I. 43 



CHAPTER n. 

OF PROPOSITIONS 



SECTION I. 

Of Judgments. 

162. A judgment is an act of the mind affirming a 
relation between two objects of thought by judgments. 
means of their conceptions. Hence in every judgment 
there must be metaphysically two conceptions and the 
act affirming the relation. The conceptions are repre- 
sented physically by the terms Subject and Predicate, 
and the act affirming the relation by the Copula, and 
the judgment thus expressed is a Proposition. 

163. It will be observed that this definition distin- 
guishes the judgment from the command. Distinguished 
the question, and the exclamation ; inasmuch ExSam^ations?' 
as no one of them affirms a relation of agree- **"• 
ment or disagreement between the terms or concep- 
tions which are included in them. Witli these forms 
of speech Logic has nothing to do, except as we shall 
see by and by the question is sometimes to Question and 
be regarded as furnishing the matter upon J"dg"^ent. 
which a judgment is sought. Thus we say " A is B ; " 
this is a judgment. But in the question ''is A, B?" 
we furnish the matter A and B, and ask for the copula ; 
or in the other form " what is A ? " we furnish the sub- 
ject and copula, and ask for the Predicate. 

164. The terms pf a Proposition are regarded as 



I 



M LOGIC. — TART I. [CHAP. 

constituting its matter. Hence judgments may be in 
the same matter thoug-h differins; in form, 

Matter and A»-n» i-t-»' a ia* i-r» 

Form of judg- as A IS ii, auQ JD IS A ; and A is not jd, or 
^^^' ' B is not A ; are all in the same matter. 

But A is B, and A is C, and B is 0, cfec, are the same 
in form though differing in matter. 

165. By the scope of a judgment we mean its com- 
prehensiveness in either continuous or discrete quantity. 

Scope of Judg- Thus " 6>7i6 man is walking," and "two men 
ments. " ^j.q walking," differ in scope ; the latter 
being twice as large as the former. Again, " men 
catch at straws," and " men catch at straws when they 
are drowning^'' differ in scope also ; the former being 
more comprehensive, since the latter limits " the catch- 
ing at straws " to some particular time or condition. 

166. Judgments have been divided into three classes 
Species of ^^ reference to the Relation which they af- 

judgments. ^Yv^ to cxist betwccn the parts of the Judg- 
ment — Categoric, Conditional, and Disjunctive. 

167. This Division corresponds with the three great 
fundamental relations of conceptions to one another — 
namely, the Substance to its Attributes or Properties, 
the Cause and its Effects, and the Whole and its Parts, 
which have been discussed in the preceding chapter. 

168. If the judgment simply affirms or denies an 
Categorical. agreement between a Subject and a Predi- 
cate it is called Categorical^ as A is B, or A is not B. 

169. If the judgment atfirms the reality of a Predi- 
conditionai. catc ou tlic grouud of tlic reality of the Sub- 
ject, the judgment is called Conditional^ thus. If A is. 
Bis. 

170. But if the judgment affirms the reality of one 
Disjunctive. of two tcrms, ou tlic grouud that the other is 
n(9^real, the judgment is csilled JJ{sju7ictive ^' thus. Either 
A or B is. If A is not B is. 

171. But in both the Conditional and the Disjunc- 
conditionai and ^ivc tlic tcrms iustcad of being single cogni- 
?iy^ morrihan tious or coiiccptions are always categorical 
two terms. judgments. Thus If A i^, B is,— is the same 



n.] OF PROPOSITIONS.— SECT. I. 45 

as if A is existing or is real^ B is existing or real. And 
so with the Disjunctives, Either A or B is existing or 
real. 

172. Now as the Conditional affirms its Predicate 
on condition that the subject is real, and the Hypothetical 
Disjunctive on the condition that it is not J^^sments. 
real ; the two judgments unite in the point of indiffer- 
ence that they both affirm under a condition {sub con- 
ditioner i^ L'TTo^ecreft)?). They are sometimes considered 
as two species o{ S^i/pothetical judgments, 

173. But as the members of both the Conditional 
and the Disjunctive jugments are, by them- presuprose ca- 
selves considered, Categorical Judgments ; mlnis^ ^''^^' 
these judgments are never primary. The judgment 
itself, that is the subjective act, is as simple as in the 
Categoric Judgments ; but there must always have 
been a Categorical Judgment before either form of the 
Hypothetical. 

174. We will therefore postpone the consideration 
of the Conditional and Disjunctive, until after we 
have examined the Categorical Judgments. 

175. Cate2:orical Judp-menis are of three categorical of 

, . I ^ Q -W three kinds. 

kinds : 

(1.) In the first place they simply affirm or deny the 
Predicate of the Subject, as A is B, or A is not B ; or 

(2.) They compare the Subject with the Predicate, 
as A is greater than B, or A is equal to B. 

(3.) They represent the Subject and the Predicate 
as sustaining some numerical relation to each other, as 
A is one-half of B, or A is three times as much as B. 

176. The first of these are Categoricals in Logical 
Quantity, which we will call Pure Categoric p^re catego- 
cals ; the second class are Categoricals in '■'''^^^• 
Continuous Quantity, and are called Com- comparative. 
parative or Relative Judgments ; and the third are in 
Discrete Quantity, and in one of their formes of expres- 
sion constitute what are called Probable Probable. 
Judgments. 

177. We will therefore consider these Judgments 



46 LOGIC. PART I. [chap. 

and the Propositions in which they are expressed in 
the following order. — (1) Categoricals in Logical Quan- 
tity : (a) simple, (b) complex, (c) compound. — (2) Com- 
parative Judgments. — (3) Probable Judgments. — (4) 
Conditional ; — and (5) Disjunctive Judgments. 

SECTION II. 

Of the Terms in a Proposition. 

178. Categorical Judgments have been defined as 
those which affirm or deny simply an agreement be- 
tween the Subject and Predicate. 

179. Since a judgment necessarily implies two cog- 
Two Terms, nitions, two terms must be contained ex- 
pressly or implicitly in every Proposition. In some 
cases there is no difficulty in finding them at once, as 
" man is mortal,'''^ But in other cases it is not obvious 
to the inexperienced at first glance what the terms 
really are. A little consideration however will always 
bring them to light. Thus if we say " John loves," 
we have for subject obviously "John ; " we predicate 
of him " loving^'^ and tj^e proposition is the same as 
" John is loving r " God exists." — Here existence is 
what we predicate of God, and we may say " God is 
existing." It is the same if we say " there is a God ; " 
" God'''' is still the subject though coming after the 
copula, and " existence " the predicate implied in the 
copula itself. Or again if we say " it rains," — " rain " 
is the subject, and that which we predicate of it is that 
it is falling, '' rain is falling." 

180. In English the subject is placed before the 
Subject placed coDula foT the most part, yet not always or 

before the Co- ^ •! a j '-i • x»l x 

puia. necessarily. And it is oiten necessary to 

know something of the connection of a proposition with 
others* or of the circumstances under which it was 
uttered, in order to decide which is the Subject and 
which the Predicate. But that is always Subject of 
which we are speaking, and that is Predicate which is 
affirmed of it. 



n.] OF PROPOSITIONS. SECT. II. 47 

181. We use the Subject chiefly with reference to 
the sphere of its conception, and the Predi- subject used 
cate with reference to its matter ; that is, in J^'Jf^^ JXVrV'''^ 
the subject we are thinking of the thing retZfncl^o'hs 
itself in its substance, and in the predicate of °^^"^'- 

its properties or what may be said of it. 

182. The Subject may be either a noun or a verb 
in the infinitive mood, as " man is mortal," what may bo 
" to err is human." But for the most part subject. 
when the subject is a verb in the infinitive mood, it is 
placed after the copula in English, as "It is hard to 
deny oneself." Here "to deny oneself" is manifestly 
the subject, and that which is said of it is that "it is 
hard." 

183. The Predicate of a Proposition may be either 
a noun denotative, or an adjective connota- what predi- 
tive, or a verb in the infinitive mood ; — as ^^®- 

" man is an animal," " man is mortal," " to be good is 
to be great." 

184. In perceiving an object we perceive it as a 
whole — substance and properties all com- objects per. 
bined in one objective reality. But by a wholes. ^ 
subsequent process of reflection and analysis we come 
to separate it in our thoughts into substance and pro- 
perties, and each of these properties may be. predicated 
of the object. We see the snow, we analyze it into 
substance and properties, we think of whiteness and 
say the snow is white ; because that property is one 
of those which was contained in our very perception 
of the snow. 

185. Any property which belongs thus to a logical 
whole, whether it be individual or universal. The formation 
may be predicated of that whole. of judgments. 

186. When a property is ascribed to a subject in 
any iud^ment, the subiect beins; taken as a propositions 

^• I'T T ^ J ^1 ' ^ ^ 1 resolvable into 

distributed term, the judgment may be re- terms, 
solved into a cognition, as " the snow is white," into 
" white snow." 

187. But when the property is ascribed to an un- 



48 LOGIC. PAKT I. [chap. 

determined part, the subject being undistributed, we 
Into Terms ^^7 rcsolve the judgment into a term, mak- 
with Modais. jjjg ^i^g Predicate an adjective, as " some 
trees are deciduous," becomes " deciduous trees." By 
this process that which in the judgment was the pro- 
perty of a genus, becomes now the differentia of the 
species included in the genus, or next higher and com- 
prehending conception. Thus by every change in our 
form of expression, and by every assertion we make, we 
change our classification. We have all noticed such 
Examples. cxprcssious as " liorsc-chestnut " and " chest- 
nut-horse, " " brandy-peach " and " peach-brandy, " 
" sand paper" and ^' paper sand." They illustrate the 
point under consideration — they invert the order of 
classification ; the noun, here as in all cases, denoting 
the genus, and the adjective, when not a mere explica- 
tive, the differentia of the intended species, which is 
really the subject of the predication. 

188. Logically, therefore, the use of an adjective 
The Logical bcfore a noun is indicative of a contained 

force of Ad jec- . • i i • i • ^^ i 

tives. species, as m the cases just given, "sand 

paper" and ''paper sand" for instance — the former 
denoting a kind of paper as distinguished from other 
kinds, and the latter denoting a kind of sand distin- 
guished from other kinds of sand. 

SECTION III. 

Of the Copula. 

189. The Copula is the formal Cause or constitutive 
Copula. of the Judgment. The effect of the Copula 
in pure categorical judgments in Logical Quantity, is 
that it includes the subject in the sphere of the Predi- 
cate ; that is, supposing the Copula to be affirmative — 
and of affirmative Copulas only will we speak at the 
present. 

190. Some Categoricals affirm an identity between 
In Identical tlic Subjcct aiid tlic Predicate. These are 

ju gments. called identical Judgments, As '' Victoria 



n.] OF PROPOSITIONS. SECT. H. 49 

is the Queen of England," "common salt is chloride of 
sodium," " a triangle is a figure with three sides," &c. 

191. But in all other cases the Copula in pure 
Categoricals includes the Subject within the 

sphere of the Predicate ; and of course shows tegSricu'if ufe 
a coincidence of sphere to the extent of the coincidencI'Vf 
comprehensiveness of the sphere of the Sub- fna^iiyVMat! 
ject, and an analogy between the spheres so 
far at least as the matter of the conception of the Pre- 
dicate extends — which is of course the Essentia of the 
Genus denoted by the Predicate. 

The simplest form of the Copula is^ — " ^5," or " are,^^ 
As " A is B." " All men are,'' &c. &c. cofS' °^ '^^ 

192. But we sometimes have the verb " to be in past 
or future tenses. '' Alexander was King of cqpuia in in- 
Macedon," — ''To-morrow will be Tuesday." transitive verbs. 
For the most part there is no necessity of being more 
precise in expressing or analyzing the Copula. But if 
there is, the thing is easily done. " Alexander is that 
which was King of Macedon^' — " To-morrow is that 
which will he Tuesday^ This destroys indeed the 
rhetorical beauty or structure of the sentence. But 
Logic takes no note of such things. 

193. Again and more frequently still the Copula is 
merged in a transitive verb. As "Fortune copuia in tran- 
favors the brave," " Fortune is that which "^'^^« v^'^^^- 
favors the hraveP — " A wise King makes happy sub- 
jects," " A wise King is that which makes haj^joy 
subjects^ 

194. Mistakes are often made in attempting to de- 
cide what is Copula and what belongs to the Mistakes to be 
terms in a Proposition. Thus if we say that avoided. 

" heat is the cause of fluidity," we must not suppose 
that '' heat " and '' fluidity " are the terms, all the rest 
being copula. The predicate in this case is not " fluid- 
ity," but the cognition expressed by the words " the 
cause of fluidity." Again, " animal includes man." 
Here it has been supposed that the predicate is in- 
cluded in the sphere of the subject. But the predicate 

3 



50 LOGIC. — PART I. [chap. 

is not " roan " merely, but " that which includes 
man ; " that is, " animal '^ is the genus which includes 
" man." 

195. In saying that the effect of the Copula in cate- 
gorical Propositions in Logical Quantity, is to include 

The Real and ^hc subjcct iu the Sphere of the Predicate, I 
Eifect^of^the ^o uot mean to say that such is the intended 
Copula. effect ; or that in forming the judgment the 

sjphere of the Predicate is at all before the mind, or 
consciously in the thoughts. Thus when I say that 
" man is an animal," I am not thinking of animals / 
that is, I am not thinking of the class of objects to 
which I refer man. On the contrary, I use the predi- 
cate as a general term — with reference to its Essentia 
and not its sphere ; not the individuals contained in it 
are the objects of thought, but simply and only the 
necessary matter of the general conception. 

196. Now this necessary matter of the general con- 
ception, as we have seen, is only the Essentia of the 
Predicate used gcuus to which the subjcct is referred. It 

s^iua'^'of^ uie 3oes uot iucludc the Differentia of any com- 
Genus. prehended species, still less of course the 

individual properties which distinguish one individual 
from another, and without which no conception of any 
one of the individuals included in the genus can be 
formed. 

197. In the act of judging the Subject is distinctly 
and conspicuously before the mind as a sphere, and the 

The Subject spheic of the Predicate is only indirectly 
Sious in°"'the ^^d remotely before the mind. Hence it is 
thoughts. j^Q sphere of the subject and the matter of 
the predicate between which the mind consciously and 
intentionally affirms the agreement. The effect, how- 
ever, is that the subject is of necessity thereby in- 
cluded in the sphere of the predicate as a proximate 
genus. 

198. Since the copula in pure categorical judgments 
Pure catego. iucludcs tlic subicct withiu a higher sphere, 

ncala make a n ... *^ i T^iii 

classification, or reicrs it to a comprehending class, the 



n.] OF PROPOSITIONS. — SECT. IH. 81 

principles of classification are necessarily implied in 
the investigation of categorical Propositions. 

As we have already defined the principal terms 
used in Classification, we shall need to resume the sub- 
ject only for the purpose of stating its general princi- 
ples, so far as they are implied in or requisite for the 
purposes of Logic. 

199. When there are more than the three grades, 
Genus, Species, and Individual, the same principle of cias- 
principle holds in the subordination of fifmoJ^tha^Ke 
classes. Thus the matter contained in the ^'^'^^^• 
conception of the Genus = Essentia, 

" Species = Ess. + 1st Differentia. 
1st Sub-species = Ess. + 1st Diff. + 2d Differentia. 
2d Sub-species = Ess. + 1st + 2d -i- 3d Differentia. 

" Individual = Ess. + 1st + 2d + 3d Dif. + Pecu- 
liarities. 

200. But besides this, each class will have proper- 
ties, and each individual accidents, which Necessary and 
are not included in the above analysis of the ?er"\nTorS: 
matter of the conceptions ; what is named ^^°"^- 
above is necessarily included in the conception. All 
else is merely contingent and accidental. 

201. It will appear from the above statement of 
subordinate spheres and their matter, that comprehensive- 
the more comprehensive of individuals the anfexcUisSess 
les comprehensive of matter any conception of Matter. 
will be ; and vice versa^ the more comprehensive of 
matter the less comprehensive of individuals. 

202. As the principles of classification are founded 
in the nature and truth of things, the Differ- ^^^^.^^ ^^ 
entia of a species must therefore always sus- Differlnlia " °o 
tain a certain relation to the Essentia of any 

genus under which it can be included. Thus the Dif- 
ferentia of " wise " and " foolish," of " pious," of 
" humane," &c., can be predicated only upon the Es- 
sentia of " man," as a genus. We can predicate 
'^ right " and " wrong " in a moral sense only of the 
acts that proceed from freedom of choice, and liaving 



52 LOGIC. PART I. [chap. 

this [freedom] as an essentia. We can predicate "hard," 
" soft," " heavy," " light," &c., &c., only of material 
things. 

203. When a word is used to denote a class, we use 
it without the article in English, as " man," &c. We 

Words denot- ^^ ^^^ ^^J ^hat " au animal " denotes merely 
wfthSut'the'ar"? ^^^^ csscutia — that which is essential to all 
tide. animals. For when the word is thus used 

with the article it denotes some existing animal with- 
out denoting precisely which perhaps, and consequently 
implies the differentia and accidents of an individual 
also. But the word " animal " when used simply and 
without the article, whether definite or indefinite, im- 
plies merely that which is essential to the animal 
nature, and by no means all that is found in any exist- 
ing animal. We can form no image in our minds 
representing merely "ammaZ/" the image must be 
of a7i animal — some animal already existing, or which 
might possibly exist — and consequently the image 
must contain in it more than is represented by the 
generic term. 

204:. The words " the animal " always refer to some 
individual animal before the mind, and consequently 
imply the individual properties necessary to 
articles f^the^" tlic couccption of the individual referred to. 
used witiTthe " A^i afiimal^^^ used as a subject, as also 
su ject. (^ animals " in the plural, always implies 

something more than the mere essentia of the genus 
''animal," since all animals and each animal must have 
some system of nutrition for instance ; and the essentia 
of such a system is always implied when we speak of 
" an animal," or of " all animals." But yet as all animals 
have not the same systems, no one individual system 
can be included in the conception. But when we use 

With the Pre- ^^^^ word "an animal" as a Predicate, the 
dicate. matter of the conception is precisely the 

same as if we had used " aiiimal " without the article, 
as " man is an animal " is merely ascribing to man the 
essentia of animal nature, just as when we say " man 
is animal." 



n.] OF PJROPOSITIONS. SECT. IV. -§3 

205. We have thus far been speaking of the classi- 
fications that are based upon those insepara- 
ble properties of objects which are the most prope?'iernot 
conspicuous. But such properties are not of^ "ciassmca- 
always or the only ground of classifications. ^'^"' 

In classifications, lor the purposes of the Natural 
Sciences, a very different principle is often found the 
most conducive to the end in view. 

206. The classifications of the Natural Sciences or 
Natural Genera or Species, are for the most 

part based on properties which are not only turaf cia'^sifi^t- 
inseparable, but also incapable of different 
degrees of intensity — of a more and a less — thus " man 
is biped." We have no such expressions as " more 
biped," " less biped," &c. So it is also with such 
words as " quadruped," " winged," " dogtoothed," 
" hoofed, " — and the words " mental," " material," 
" eternal," " infinite," &c. They have no comparatives. 
It is the same with the mathematical differentia, " tri- 
angular," " quadrilateral," " circular," " elliptical," 
" conical," &c. 

207. But besides this it is obvious that any mode 
or separable accident whatever, may be the j^ogicai ciassi- 
ground or principle of a mere transient ^cations 
classification. Thus we may classify the inhabitants 
of a city into sick and well — those in a room as those 
that are sitting, and those that are standing, &c. The 
mode or accident which serves as differentia to these 
transient classifications must, however, be such that 
the terms denoting its presence and absence cannot be 
both predicated of any one individual at the same mo- 
ment of time and in the same respect. 

208. It will follow from what has been said, that if 
any individual contains the Differentia of mdividuaia 
any species, it must be included in that spe- cfuleTiil^spe- 
cies ; and if either individual or species con- *^^®^- 
tains the Essentia of any genus, it must be contained 
in that genus. The Differentia are essential to the 
specieSj and the Peculiarities to the individual. The 



64 LOGIC. PART I. [chap. 

peculiarities also are the differentia of the indivi- 
dual. 

209. Hence every assertion we make bj the neces- 
sary laws of thought or of affirmation, makes a classifi- 
cation. It refers the subiect to a class whose 

All assertions , . t rv* , > i . i 

classify their csscntia or diiierentia, as we may regard the 
6u ject. class, a genus, or a species, is denoted by the 

predicate. We say that '' this man is a farmer ; " we 
refer him to the class of farmers. We say " the snow 
is falling ; " we refer it to a class of things whose dif- 
ferentia or essentia is denoted by the state expressed 
by the predicate " falling." We say *' God is good ; " 
we refer Him to the class of objects which are charac- 
terized by the attribute or property of goodness. We 
say " the wicked will be punished ; " we refer them to 
a class, whose only point or property in common it 
may be, is the doom that is declared by the predi- 
cate to await them ; and yet this point or property is 
made, pro hac vice, the ground or basis of a classifi- 
cation. 

210. But by the very nature of the case we cannot 
make an assertion without referring the subject of 

. which we speak to a class ; and every time we 
mem^iasiififs spcak of it iu a different connection, to a 
new class — the differentia of which is ex- 
pressed by the predicate we use. If we call a man, 
brave or a coward, honest or a knave, wise or ignorant, 
good or bad, polite or rude ; — if we say of him, he is 
standing or walking, sitting or sleeping, all these classes 
are called up before the mind, and every new assertion 
concerning any subject of which we are speaking, like a 
fresh turn of the kaleidescope, groups and classifies all 
things anew. And upon this classification depends 
alike the cogency of an argument, the merriment of 
. . humor, and the keen relish of wit. Even a 
dicrous cTassifi- jest is but a ludicrous classification. A sar- 
casm does no more than to class one Avith per- 
sons and things that are contemptible, and a bad name, 
a disgraceful epithet, a conviction of wrong, brings 



II.] OF PROPOSITIONS. SECT. IV. 55 

upon one only the differentia of the species to which 
he is thus referred. 



SECTION IV. 

Of the Adequacy of Projpositions. 

211. Let us now consider some of the principles 
and laws of predication with reference to the adequacy 
of Propositions, as expressions of the judgments which 
they represent. 

212. A Proposition for the purposes of Logic should 
be like the testimony given under the Com- Adequacy of 
mon Law oath in civil suits, " the truth^ the Propositions. 
whole truth^ and nothing hut the truthP 

(1.) Of any obiect or class of obiects, its Name and oe- 

1 -J. J i* -i.* i? 1. finition Predi- 

name and its denmtion may oi course be cated. 
predicated. 

(2.) Synonymous terms may also always be predi- 
cated of each other. But any two or more synonymous 
names, which are not mere individual names, '^^'^°^^' 
and which may be predicated of the same object of 
thought, must denote Alternate Conceptions of that* 
object, and are not likely to be predicable of each 
other. 

(3.) Of any general term, that is, a term denoting a 
genus, we may predicate any term denoting of a Genus. 
the essentia of the genus, or any one of the essentia in 
an abstract term, or by a connotative adjective. 

(4.) Of the Species we may in the same way predi- 
cate not only the Essentia- of any higher and Essentia of 
comprehending genus, but also its own Dif- ^p^^'es. 
ferentia. 

(5.) Of any individual we may also in the like way 
predicate the Essentia of any genus in which of the indi- 
it is included, the differentia of the species ''*'^'^^' 
to which it belongs, and the peculiarities of the indi- 
vidual (inseparable accidents). 

(6.) Whatever may be predicated of each individual 



56 LOGIC. PAST I. [chap 

ofindividuais ill SL class, may be predicated of the class 
as a whole. Thus if each individual man 
has two feet, then " man is a two-footed order of 
beings." 

213. Besides the above there are always properties 
Accidental Pro- which arc uot regarded as either Essentia or 
perues pre i- j)jffgi,^j^|i^^ ^q ^^]} ^g Separable accidents 

which constitute the various modes or conditions of 
being, that may be predicated of any subject when- 
ever we have any sufficient reason to affirm them of it. 

214. If the subject denotes any real or possible 
predicdtea of thins:, theu the Predicate may be a positive 

real and possi- .it i i j^i i • 

bie Subjects. term and denotes some property that is pre- 
dicated of it. For if it be a possible or a real thing, we 
can say " it is possible," " it is real." But if it be an 
impossible thing its predicate must be a negative term, 
since no property or mode can exist without its sub- 
stance ; thus if the conception denoted by the subject 
A be an impossibility, we can say that " it is impossi- 
sible." 

215. Whenever a given predicate is to be used 
Alternate Con- that Alternate Conception of the subject 
^eptionsassu - gj^^^^^^j ^^ uscd, wliicli reprcscuts it by the 

matter on account of which it is contained in the genus 
denoted by the Predicate. 

216. Alternate Conceptions represent the same ob- 
ject by different matter. But the subject is included 
in the sphere of the Predicate, only because it has the 
properties which constitute the Essentia of the genus 
Examples. dcuotcd by thc Predicate. Thus, Washing- 
ton as General commanded the American Army ; gave 
Commissions to the Officers in the Army and Navy, &c. 
But as President he presided over his Cabinet, nomi- 
nated Civil Officers, sent Messages to Congress, pos- 
sessed the Veto Power. But it would be logically 
faulty to say, " the A^nerican Goininander ate his 
breakfast," for instance ; for as Commander he did not 
eat, but it was simply as George Washington that he 
ate. So it should not be said of an act in his military 



n.] OF PKOPosmoNS. — sect. iv. 67 

command, — the President did it ; for as President he 
did not do it, but only as Commander did he do it. 
Nor should we say George Washington vetoed this 
bill, for not as George Washington but as President 
Washington did he possess the veto power, or exer- 
cise it. 

217. Words denoting titles and ranks are however 
but Alternate Conceptions of the individuals Titles, 
to whom they are given, and custom has so far not only 
sanctioned, but required the use of a man's title even 
when we are speaking of his personal acts and proper- 
ties, that a disregard of the usage would be regarded 
as discourteous if not as intended for an insult. 

218. The subject of any proposition should always 
be so comprehensive as to include all the . comprehen 
individuals to which the predicate used in subject *^^ ^^^ 
the proposition is applicable. 

219. This condition is often violated for rhetorical 
purposes ; nor does its violation necessarily Rhetorical 
involve an error in the conclusion, though it violations. 
renders us liable to fall into one. Thus we say " the 
Papists hold to the supremacy of the Pope," which is 
correct. But if we say " the Papists believe in the 
Divinity of Christ," we say what is indeed true ; but 
as other Christians believe in that dogma also, our sub- 
ject is of too narrow a comprehension, and suggests 
the inference that a belief in the Divinity of Christ is 
one of the differentia of the Papists. Although there- 
fore there may be cases in which the violation of this 
rule does no harm, yet unless there is something in the 
context or in the circumstances under which the rule 
is violated to guard against the error, the rule must be 
strictly adhered to, or our proposition does not state 
" the whole truth." ^ 

* I have before me a case in point. In an infidel author, whom I need 
not name, there is an accumulation of statements designed to show that the 
Scriptures, as we now have them, cannot be relied upon as inspired. He says 
of the Scriptures (his subject), " the oldest manuscript does not reach back 
to within centuries of the origin which the Scriptures claim for themselves. 

3* 



58 LOGIC. PART I. [chap. 

220. When the Predicate is a general term and not 
a mere connotative of some accident of the subject, the 

accidents of the subject are not included by 
the'^suKt in- mcaus of the proposition in the matter of the 
scopi of thi Predicate. Thus when we say, " the rich 
ju gment. ^^^ auxious," wc take no notice of the color, 
size, or any other accident of the persons included in 
the word " rich." If we say " John is sick," this im- 
plies nothing concerning his accidents, and 
cidlntY^of the uo councction of the Predicate with them ; 
ciVed iTthe the Predicate is affirmed of what is essential 
Ju gment. ^^ ^j_^^ subjcct as such and not of any of its 

accidents — that is, what is essential to it as a subject, 
and not what is necessary to its reality.^ 

221. But whatever term is predicable at all of either 
individual species or genus, must be predicable of the 

individual or individuals (if the subiect be 

The Predicate ..-i .r> • i. \ j. • 

must include Cither a specmc or generic term), as contam- 

the necessary . • ii • j. • i. i. 

matter of the lug lu tliis couccptiou whatcvcr IS ucccssary 
Subject. ^^ their existence as individuals, species, or 

genus as the case may be. 

222. Thus if we say " This mountain has existed since 
the creation«of the world," we are understood to say 
not merely that the matter of which it is composed has 
existed so long, but that that matter has existed not 

It is written in a letter entirely different, now divided into words, surrounded 
by points indicative of the meaning and punctuation of words, divided up 
into chapters and verses, and the manuscripts abounding in various readings, 
interpretations, omissions, and corruptions." But the author does not state, 
and the unlearned reader does not know, that precisely the same thing 
could be predicated of the text of Herodotus, Thucydides, Livy, Tacitus, 
and in fact of every ancient author, and yet no one ever doubted the 
genuineness of the works which are received under those names on that 
account. If he had made his subject as comprehensive as the Predicate 
would allow, and included these works with the Scriptures in his Proposi- 
tion, it would have destroyed the effect which he designed to produce. 

* The scholastic writers expressed this distinction by the use of the abla- 
tive pronoun qua. The subject qua subject — this expression is also used to 
distinguish between the different predicates which any object of thought 
may have when represented by its Alternate conceptions. Thus Washington 
qua President possessed the Veto Power, qua Commander-in-Chief gave 
Commissions to the Officers of the Army and Navy. 



n.] OF PKOPOSITIONS. SECT. V. 69 

only as mountain [the species], but also as this indi- 
vidual mountain with its inseparable accidents. So 
when we say "men are immortal," we mean not only 
that what is essential to humanity, but also whatever is 
distinctive of each individual as an inseparable acci- 
dent is included in the immortality ; so that men will 
exist there individually, distinct and distinguished by 
the same inseparable accidents of personality as 
here. 

223. For rhetorical purposes this rule also is often 
violated. In all those figures of speech called Rhetorical vio- 
Metaphor, Trope, &c., these rules of Logic ^^^^°°^- 

are departed from for rhetorical purposes. It becomes 
necessary therefore to consider in all cases whether the 
word used is the real subject, or merely some figure 
of speech used in its stead. 

SECTION V. 
Of the Quantity of Propositions. 

224. The scope of the judgment is not important to 
its deductive force or position in a syllogism, since 
whether it includes much or little in a numerical esti- 
mate it goes in for what it is. 

225. But the Logical Quantity is of the utmost 
importance, since that indicates its relative importance of 

i.jjx • j.1,1 i? J' auantity of the 

amount and determines the laws oi predica- Terms. 
tion and deduction. 

226. Logical Quantity in its broadest sense is of 
three varieties, — (1) comprehensive : (2) in- Three oimen- 

. . -, fU,. ^ ^ , ,^ J \ J sions of Logical 

tensive ; and (o) protensive. Quantity. 

(1.) Comprehensive, or Extensive Quantity, is the 
comprehensiveness of the sphere of the con- . comprehen- 

\ ^ sive. 

ception. 

(2.) Intensive Quantity is measured by the amount 
of matter in the conception. intensive- 

(3.) But we have also a Protensive Quantity brought 
in by the consideration that the facts included protenaive. 



60 LOGIO. PART I. [chap. 

in the sphere of any conception are not always actual 
facts at the same moment of time. If we say " all men 
are mortal," we mean to include in our category not 
only all men now living^ but all who have lived in time 
past or will live in time to come — all beings that are 
men. But a predicate may be ascribed to a subject at 
one time, or as true of it at some times, which could 
not be ascribed to it with truth at others. 

After having thus named this variety of Quantity, 
we shall leave it out of consideration for the present, 
and proceed to consider Comprehensive or Extensive 
Quantity in reference to judgijients. 

227. In reference to the object now before us Inten- 
intensiveQuan sivc Quantitv is unimDortaut in itself, and is 

tity determined i i . » iiii /^ i 

bythecompre- always Qetermined by the Comprehensive 
quantity being always in the inverse ratio 
s/med^'a1)so'- ^^ ^^' Thc Protcnsivc quantity is assumed 
lute. ^Q ]jQ absolute ; that is, to include all time — 

and the same as if it were expressed by the word 
" always^^ as " All A is always B ; " " Men are always 
mortal." 

228. There are three dimensions of Comprehensive 
Three Dimen- Quantitv, accordiup; as the subject of a iuds;- 

sions of Com- ^ , »^ ' t /-, x^ • j • • j i rc\\ i 

prehensive mcut may DC ; — (1) an maividual ; (2) several 
Quantity. individuals considered as a part of a class, 
not denoted by any term which constitutes them a 
species within that class ; or (3) several individuals con- 
sidered as constituting a class, species, or genus. 

229. The first class are called Individual judg- 
ments ; the second Particular judgments; and the 
third are called Universal, 

230. It is obvious that on these principles of divi- 
sion, and in reference to Quantity, there can be but 
three Species ; for a judgment must be either of one^ 
of sorae^ or of all. If we say that, " some " may in- 
clude many or only a few ; nearly all or only two ; we 
do not thereby constitute a Logical whole. 



n.] OF PROPOSITIONS. — SECT. VH. 61 

SECTION VI. 

Of the Quality of Judgments, 

231. The Copula of a Judgment may be either 
(1) affirmative, or (2) negative; that is, we .Three Quau. 
may say A iibs) B, or A {is not) B. The first tloL^^ I'roposi- 
A is B, includes A in the sphere of B, and is an Affirma- 
tive judgment ; the second A is not B, excludes A from 
the sphere of B, and is a Negative judgment. But B 
and not-B are antithetic terms. They denote spheres 
which are the complements of each other. Hence if 
A is not in the sphere of B, it is in the sphere of non-B ; 
and we may say that A is non-B. This is called (3) an 
Indefinite judgment. Hence three varieties in refer- 
ence to Quality — 1st, includes the subject in the sphere 
of the Predicate ; 2d, excludes the subject from the 
sphere of the Predicate ; the 3d, includes the subject 
in the Negative sphere connoted by the Predicate of 
the Affirmative. 

It is obvious that in reference to Quality there 
can be no other species of judgments than these 
three. 

SECTION VII. 

Of the Modality of Judgments. 

232. In reference to the certainty of the Judgment, 
we may have three kinds of judgments ; — Three mocIcr 
Prohlematical^ Assertive^ and Necessary^ or ofproposnions. 
Apodictical. This is called the Modality of Judg- 
ments. 

(1.) The Differentia of the Problematical is that 
they merely affirm that the subject may be problematical. 
in the category of the Predicate, or the possibility of 
the Proposition being true. 

(2.) The second is called Assertive; — they affirm 
the truth of the judgment as a matter of fact Assertive. 
and reality. 



m 



LOGIC. — PAKT I. 



[chap. 



(3.) The third are called Necessary or Apodictical ; 
Necessary. they affirm that the truth could not be other- 
wise — as when we say " two and two make four." 



SECTION vm. 

Of the Four Cardinal Propositions. 

233. Combining Quantity, Quality, and Modality, 
Twenty-seven wc havc the foUowiufi^ table of Catesioric 

Categorical t j i 

Judgments. J udgmCntS. 

{Problematic. 
Assertive. 
Apodictic. 
i Problematic. 



Categoric ^ 



Individual 



Particular 



Universal 



Negative < Assertive. 

( Apodictic. 

\ Problematic. 
Indefinite •< Assertive. 

( Apodictic. 

\ Problematic. 
Affirmatives Assertive. 

( Apodictic. 

i Problematic. 
Assertive. 
Apodictic. 
i Problematic 
Indefinite •< Assertive. 
( Apodictic. 
( Problematic. 
Affirmative \ Assertive. 
( Apodictic. 
( Problematic. 
•< Assertive. 
( Apodictic. 

{Problematic. 
Assertive. 
Apodictic. 



Negative 



Indefinite 



II.] OF PROPOSITIONS. SECT. VIII. 63 

234. But as Problematical judgments never enter 
as Premises into any Argument merely as Problema- 
tical, we may omit them from any further consideration 
at present. 

235. Again the difference between the Assertive 
and the Apodictic or Necessary has no effect 

upon the general principles of deduction. daisVeduceS'to 
If a Proposition be true, that is all that is 
required, the modality of its truth being wholly unim- 
portant. We may take the Assertive therefore for all 
our purposes, neglecting the difference between that 
and the Necessary. 

236. But again, the Negative and the Indefinite 
sub-species are the same so far as all the 

1 J I* J J J.' The three Qua- 

laws and purposes oi deduction are con- iities reduced to 
cerned. For since the Positive and the 
Negative Spheres are complements of each other, to 
exclude from the Positive (which is the differentia of 
the Negative) is the same as the inclusion in the 
Negative sphere (which is the differentia of the Inde- 
finite). 

237. Again in respect to Quantity the Individual 
and the Universal are alike, in that the sub- 
ject (in which alone is found the differentia auantities re® 
of Quantity) is in both of them a logical 

whole. Whether an individual or a class, it is imma- 
terial for all the purposes of deduction, so long as it is 
a logical whole. Hence we consider Individual judg- 
ments the same as Universal for all the purposes of 
deduction. 

238. But a Universal Judgment may be either 
Negative or Affirmative, and so likewise ^ . 
may a Particular judgment. We have only auaift? ' ^com- 
four cardinal judgments which we need con- 
sider. These are Universal Affirmative, Universal 
Negative, Particular Affirmative, and Particular 
Negattve. These may be considered the four cardinal 
Propositions in Logical Quantity. 

239. As these occur so often, writers on Logic have 



64 LOGIC. — PART I. [chap. 

generally designated them by the first four vowels of 
the Alphabet. Thus 

U. A. All A is B, is represented by A 

U. N. No A is B " " " E 

P. A. Some A is Bis " " I 

P. K Some A is not Bis " " O 

These are all Categorical, all Assertive, and differ only 
in Quantity and Quality. 



SECTION IX. 
Of the Distribution of Terms, 

240. When a term is taken into the scope of a 
judgment as a logical whole, it is said to be distributed 
in the judgment ; but if it does not enter in as a 
logical whole, it is said to be undistributed in the 
judgment. 

241. It is immaterial whether the part of the whole 
Undistributed bc a large or small part, '' many " or " few ;" 
^ ^^^^' and these words therefore indicate an undis- 
tributed term as well as " some." 

242. So also we may say " some," when we mean 
" some at least and possibly all ; " or when we mean 
" some but not the whole." But the undistributed 
term as such indicates nothing of the kind, and if any- 
such modification of the term is intended, the Proposi- 
tion expressing it becomes a compound one [either 
copulative or discretive], expressing two judgments 
in fact and not one merely. 

243. The conception represented by an undis- 
tributed term is not a logical whole, and the term itself 

Not Logical must necessarily be a general one. But if 
Wholes. ^^ term denotes a part of the whole, con- 

ceived as a sjpecies^ it is no longer undistributed ; for 
the part conceived as a species becomes by the very 
fact of its being so conceived a logical whole. 

244. Hence the word "so7?iej^^ though generally 



n.] OF PROPOSITIONS.— SECT. IX. 66 

used to denote an undistributed term in the subject, 
is not an infallible indication that the term is undis- 
tributed. Thus in the illustration given by Mistake of the 
Sir William Hamilton, " some stars are all forceofsome." 
planets " (all the planets are stars). But one must have 
a conception of those stars as a class, which are planets, 
and as distinguished hy the differentia of planets, or he 
could not say that they were all the planets that there 
are among the stars. If therefore there ever was, or 
ever should be such a Proposition, except when got up 
for the purpose of seeing what one can do, the subject 
must be regarded as distributed, notwithstanding the 
usual signs of an undistributed term. 

245. There are three ways of ascertaining whether 
a term is distributed or used distributively Three ways 

/_, V -n , 1 . "^ of distnbution 

m any proposition or not. — (1) Joy the nature of terms. 
of the term ; (2) by a modal sign ; and (3) by its 
position. 

446. A term is distributed by its nature when it is 
used to denote any individual obiect, such By the nature 

J 1 "^ D of the term. 

as proper names oi persons, places, &c. 

Terms are distributed by signs in three By signs. 
ways. 

^ 247. (1.) The particles " the,'' /' this^' " that,'' by 
pointing out a particular individual in a class, "The," "this." 
of which the predicate is affirmed, make the ^""^ " '^^^•" 
term distributed ; since the force of these particles is to 
include only the one of the individuals comprehended 
within the genus thus pointed out in the scope of the 
judgment. 

248. (2.) Such words as ''all," ''every," &c., dis- 
tribute the terms ; in fact they are the most ..^ii,'' "eve- 
usual signs of a distributed term used in the '^'" '^^• 
subject of a Proposition. 

249. " All " of course clearly and expressly includes 
all of the individuals included in any genus within the 
scope of the judgment. 

250. As ''all," so also "every" indicates a dis- 
tributed term, since it necessarily includes all the indi- 



66 Loaic. — PART I. [chap. 

viduals of the logical whole within the scope of the 
judgment. All is indeed sometimes a col- 
tween'^^"'^Aii,;' Uctive rathcp than a distributive sign. Thus 
if we say " all these trees make a fine shade," 
it is most likely that we mean to take " trees " as a 
collective term rather than as a general term ; that we 
have predicated of them taken together as a collective 
whole, what could not be predicated of each of them 
individually. This difference is unimportant to the 
purposes now before us, but it will be seen by and by 
that it lies at the bottom of a most serious fallacy. 

251. (3.) Two pronouns, as "he who," and "they 
Two Pronouns that," arc clcarlv indicative of a distributed 

distribute the ^ * , cc i i i j_i i 

Subject. subject, as " lie who transgresses tne law 

commits a sin," — " who so transgresses the law com- 
mits sin ; " these forms of Propositions clearly include 
the whole class denoted by the specific term, whose 
differentia is given in the words " transgresses the 
law," in the scope of the judgment. 

252. (4.) Again, we have another class of signs, 
which, although they do not cause the general term to 
be included as a whole in the scope of the judgment, 
constitute it what is called a distributed term. These 

"Each" and tcrms arc such as " each^^ " any ; " for while 
" -^"y" by their force they apply the predicate of 

the proposition to one individual of a class only, and 
sometimes in such a way as that it can be applied to 
one only at the same time, yet they imply that before 
any actual predication it is applicable to thqm all and 
every one of them taken individually, although it may 
cease to be so the moment it has been predicated of 
one. Thus if we say of a young lady, " any man 
would marry her ; " — " man " must be taken as a dis- 
tributed term, though it is not supposed that more than 
one man will actually marry her. 

253. (5.) The indefinite article " a " also sometimes 
The Indefinite distrlbutcs the subjcct in the same way, thus 

"^•" " a poison destroys life ; " that is, " any poi- 

son," or " all poisons destroy life." 



n.] OF PROPOSITIONS. SECT. IX. 67 

254. In all Negative Propositions the Predicate is 
taken as a Whole."^ The differentia [charac- ^y position the 
teristic] of Negatives is that they exclude S'e'gt'tTve judg^ 
the subject from the sphere of the Predicate. °^^"^^- 
They do not merely partly exclude it, they may exclude 
merely a part of the subject, but they must exclude the 
subject whether as a whole or as a part from the whole 
of the Predicate, " No vice is commendable." If now 
among all the things that are commendable one vice 
can be found, the Proposition is not true. Hence it 
distributes the Predicate or speaks of it as a whole. 
Or if we say " some men are not brave," which is a 
Proposition in O, the same is found to be the case 
with the Predicate. We here mean that among all 
the things that are " brave," the " some men," are 
not included. 

255. But the Affirmatives do not necessarily dis- 
tribute the Predicate. If I say that A is B, 

all that is affirmed thereby is that A is in B, not '"dVtrfbute 

A, r»T^A' • ijj'^^e Predicate. 
IS some part oi ii. A is mcluaed m 

the sphere of B. But B may include much besides A. 
" Men are mortal ; " but men are not the only things 
that are mortal. The sphere of " mortal " is not coin- 
cident and identical with that of '' man," — it is much 
more comprehensive. Hence in A we do not speak 

* Sir William Hamilton id his new method of Notation, insists that there 
may be Negative Judgments with undistributed Predicates. 

But besides the proof given in the text of the position there taken, we 
may say further that his doctrine directly contradicts the old axiom, " it is 
impossible for a thing to be and not to be at the same time." For suppose 
S is not P and P not taken as a whole, the sphere of P as of any term is 
determined by its matter ; and the subject S is included in it if it possesses 
the matter of P and excluded from it if it does not. Now suppose that S 
has not the matter of that part of P which we take into the scope of our 
judgment, when we say S is not P, and the judgment S is not P is true. 
But suppose it has the matter of the part of P, not taken iato the scope of 
the Negative judgment, and then we have S is P ; — 

that is, S is not P, 
SisP, 
and P is P, 
and P is not P. 



68 



LOGIC. 



■PAKT I. 



[chap. 



of the predicate as a whole. The predicate is undis- 
tributed. 

256. For the same reason we do not speak of the 
Predicate as a whole in I. " Some men are black ; " 
we do not speak of " black things " as an entire class, 
comprehending no more than the " some men " of 
whom we were speaking. 

257. Hence the following Rales for the Distribution 
Rules. of Terms by position. 

1. All universal Propositions distribute the Subject. 

2. All negative Propositions distribute the Predi- 
cate. 

Or more definitely : 

A distributes the subject. 

E " both the subject and predicate. 

I " neither. 

O " the predicate only. 

258. Various devices have been resorted to, to repre- 
iiiustrations. scut by somc diagram these various Judg- 
ments or Propositions. Many of them are ingenious 
and useful, but all are liable to misapprehension, aris- 
ing from the nature of the case and the difficulty of 
representing any mere conception by actual forms. 

The following is perhaps as good as any that can 
be given. It is substantially Euler's : — 

A. — All S is P, in which case 
one circle S is included wholly in 
the other as P, but does not oc- 
cupy the whole of its sphere. 

E. — No S is P, in w^hich case 
one circle S is wholly excluded 
from the whole of the other P. 

I. — Some S is P, in which case 
we have two incomplete circles 
S and P, cutting each other so 
as to have a part x common to 
both. 






n.] OF PROPOSITIONS. SECT. X. 69 

O. — Some S is not P, in which 
we have an incomplete circle, S ^/^ 

not included in any part of the 'v_ 

complete circle P. 

259. One difficulty attending the above diagrams 
is, that they represent in A and I the sub- jy^^^^^ ^^ 
ject as constituting a definite part of the "^^°^ "^^°"' 
Predicate, or occupying an ascertained portion of its 
sphere, whereas the judgment does not so represent 
the spheres. 

260. It will be noticed that in A when the sphere 
of S becomes so large as to fill up and occupy . The predicate 
the whole of P, the Predicate has become Sisuihy^V^^ 
distributed and is taken as a whole. The spheres are 
then coincident and identical. 



SECTION X. 

Of Immediate Inference. 

The form Judgments expressed by the Proposi- 
tions A, E, I and O, which we have just examined, 
have certain relations to each other which it is impor- 
tant to examine. 

261. Such is the relation of judgments to each 
other, that no judgment can be true without g^ery judg- 
implying the truth of some other judgment, SLr.'"^^^'^^ 
either in th'e same or in the opposite Quality. 

262. These judgments which are thus inferred from 
others, as from All A is B, we infer that immediate in- 
some A is B, and that " some A is not B " ^^'^""^• 

is not true, are called by Kant " Syllogisms of the Un- 
derstanding." I shall prefer, however, to adopt the 
more English name of ImTuediate Inference, 

263. I call it " immediate " because the inference 
or conclusion is drawn without the interven- why so caiied. 
tion of that medium or middle term, which is always 
necessary in the complete Syllogism, as will be seen 
hereafter. 



70 LOGIC. PART I. [chap. 

264. By Immediate Inferences then I mean all those 
inferences or conclusions that can be drawn from any 
Proposition without the intervention of any other matter 
or term than was given in the Proposition itself. And 
as it will be the most convenient to point out these 
Inferences as we examine the Opposition, Permutation, 
and Conversion of Propositions (since it is by these 
means that the Inference is made), I will keep them 
in mind as a subordinate object while discussing these 
topics. 

I. Of the Opposition of Judgments. 

265. (1.) A and E being Universals, I and O are 
Subalterns. Called iu reference to A and E their Subal- 
terns, I being subaltern to A and O to E. 

(2.) A and E in relation to each other are Con- 

Contraries. tTaTieS, 

Sub-contraries. (3.) I and O are Sub-contraries, 

266. (4.) E and I as likewise A and O are Contror 

Contradictories. dlCtOTieS tO Cach Othcr. 

267. If now a Universal be true its Svhaltern must 
be true also. If All A is B, Some A is B, is true as an 
Inference from Immediate Inference, and if the Subaltern 
Subalterns. \^^ ^^.^^ ^j^^ Umversal as a Problematical 
Judgment is true also, as an Immediate Inference ; that 
is, If Some A is B, all A may be B. 

268. Of the Contraries only one can be true in the 
From Contraries, samc matter, tliough botli may be false. 
Hence If A is true E is false as an Immediate Infer- 
ence, and vice i^ersa ; that is, No A is B, then All 
A is B is untrue, although of course Some A may 
be B. 

269. Of Contradictoi'ies both cannot be true or false 
From Contra- in the samc matter. Hence If E is false I 
»c ones. jji^gt; ]3e truc, and vice versa. If A be false 

O must be true, and if I be false E must be true, and 
if O be false A must be true as Immediate Infer- 
ence. 



U.j OF PROPOSITIONS. SECT. X. 71 

270. The Sub-contraries may both be true in the 
same matter. If some A is B, some A is sub-contraries 

, x~» 1 1 J. cannot both be 

not B, may also be true. false. 

271. But the Sub-contraries cannot both be false in 
the same matter. 

272. We may represent the rela- ^ contraries e 
tion of these four Judgments by the ^ ^ %^ ^ 3 g^ 
following diagram, in which it will % ^ ''^^ % %^ 
appear that the sub-contrary of any '^ | ^©^"^^ \. § | 
subaltern is the contradictory of its ^ , , > ^ 

-TT. 1 T'p.T /» . I suD-contranes O 

U niversal ; and 11 thereiore two con- 
tradictories cannot be false at the same time, then 
a fortiori the two sub-contraries cannot. 

273. The subject in each of the sub-contraries is 
undistributed, and the more nearly it ap- Ratio of Qua- 
preaches to the Universal in one quality in ^'^y- 

any case, so much the more nearly does it approach it 
in the other. Thus the more nearly Some A is B is to 
All A is B, so the more nearly is Some A is not B to 
No A is B. 

II. Of Contka-Position or Permutation of Quality. 

274. The same judgment may be stated in either 
quality. Affirmative or Negative as we choose, by 
means of Negative terms and copulas. 

275. In reference to this fact we will call the first 
form in which a judgment is stated, or rather that form 
which states the judgment in the Proposition of the 
same quality as the judgment itself, the Ex- . ^^ 
posita / and that form of the Proposition contra posita 
which states it in the other quality, the Con- 
tra-posita ; and the change itself we call Contra-posi- 
tion or Permutation. 

276. Thus let us suppose in the first place that we 
have the Negative Proposition '' A is not B," illustration. 
or " No A is B." In this case we have simply ex- 
cluded A from the sphere of B, and thus denied of it 
the matter of the conception B. But since the Negative 



73 LOGIC. PART I. [chap. 

of B or non-B is the complementary sphere of B, what- 
ever is not in B is in non-B, and consequently whatever 
has not the Essentia of B must have that (if there is 
any) of non-B. Hence " A is not B " is equivalent 
to " A is non-B," — " non-B " being a Negative term ; 
and But A is non-B is an Affirmative Proposition with 
a Negative Predicate. 

277. Hence from a Negative Exposita with an 
Affirmative Predicate we may always permute into 
Contra-posita, by substituting for the Positive Predi- 
cate its Privative or Negative, and dropping the Nega- 
tive from the Copula. Thus " if man is not wise," he is 
" ^^^^wise ; " if he is " not free " he is a " slave." 

278. But if the Predicate is a Negative or a Priva- 
Negative or tivc tcrm iu thc Exposita, we have to substi- 

diclte*''^ '^" tute for it its Affirmative, and drop the 
Negative from the Copula also. Thus we may say that 
" Centaurs are not impossible," then " Centaurs are 
possible." 

279. The same holds true of the subject when the 
Predicate denotes a reality and not a possible only. 

When true of Wc may substitutc for the subject its anti- 
the Subject. thetic in the opposite Quality by dropping 
the negative from the copula, always remembering that 
the term substituted is an undistributed term. 

280. But since no property or mode can exist or be 
real without its substance^ the Predicate may denote a 
property which has no existence. In that case there 
can be no Contra-posita by means of the negative sub- 
ject ; thus if one should say " horses are not Centaurs," 
we could not therefore say " some not-horses are Cen- 
taurs," for this would imply the reality of " Centaurs." 

281. But if the Predicate be a reality at all we 
may always say, if A is not B some non-A is B. 

Let " holy " be the Predicate and " man " the Sub- 
lUustraUon. jcct, " uo man is holy," or in the other form 
" all men are not holy." 

If now we connect the negative with the subject 
no-man," this is no longer the same term taken in a 



u 



II.] OF PKOPOSITIONS. — SECT. X. 73 

different sense, but it is a totally distinct term. It in- 
cludes nothing that was included in the first term 
" man^'' and precisely all that was not included in it. 
It includes whatever is not '^ man." Of these things 
manifestly not all are holy, although if there be such 
a thing as holiness, and if it do not belong to man, it 
must belong to something that is not man. Hence we 
may say " some not-man is holy." 

282. If, however, we connect the negative with 
" holy," and say " All men are not-holy or i^Tiholy," 
the term represents an entirely different cognition from 
the term " holy." But the new term must be regarded 
as undistributed, for we do not mean to say that man 
is all that is " not holy," or that whatever is " not 
holy " is " man." And yet if our first Proposition is 
true '' some thing not holy " is " man." 

283. In the use of intelligible signs we may use 
the Privative instead of the Negative in the privative used 
Predicate, since the nature of the subject [fveinW^pftl 
limits the range of the thought or judg- ^^'"^^^• 
ment to the proximate genus. Thus for " man is not 
holy," we may substitute the privative Predicate, and 
say "man is '^^?^holy;" the subject "man" limiting 
the scope of the judgment to the proximate genus to 
which the capacity for holiness is an essentia, and also 
a differentia in the next higher subaltern genus. 

284. But when we change the Quality by changing 
the subject we may not use the Privative, But not in the 
since there can be no a priori necessity that subject. 
the Predicate should be predicable of some one indi- 
vidual in the proximate genus to the subject, or in 
any genus below the summum' or absolute whole of 
realities. 

285. If the Exposita be Affirmative we change the 
quality by means of two negatives — two permutation 
negatives in English making an affirmative, of Affirmauves. 

286. This change of the quality of Affirmatives by 
means of two negatives may be effected in three 
ways. 



74 Loaic. — PART I. [chap. 

(1.) With two negative copulas, as " there is no A 
1st case. that is not B," consequently All A is B. 

Thus " there is no man without [that has not] sin," or 
" all men are sinners." 

(2.) The second form is with a negative copula and 
2d case. a negative Predicate. " All A is not non-B," 
or " No A is non-B ; " as " No earthly creature is im- 
mortal." 

287. In this case the whole of the subject is ex- 
cluded from the Negative sphere^ and must therefore 

Privative for ^^c iucludcd iu the Positive which connotes 
Negative sphere, ^^q Ncgativc. A Privativc term will answer 
just as well as the Negative, since the subject always 
confines the judgment to objects included within its 
own sphere, which becomes for this purpose a proxi- 
mate genus, of which the Positive Predicate and its 
Privative are the coordinate parts. 

(3.) By a negative copula and a negative subject 
3d case. uscd distributivcly, we have I by contra- 

position. As " No one who has not enough is rich." 
Here '' one who has not enough," or '' all who have 
not enough," is a negative term, and the judgment is 
the same as " some [perhaps all] who have enough are 
rich" (see 277). 

288. This form however states something more than 
I, since it w^ould never appear from the fact that 
" some who have enough are rich," that '' no one who 
has not enough is rich." „ , 

289. The course of this investigation shows that 
we may always have from any Exposita its contra-posita 
by Immediate Inference. 

III. Of the Conversion of Propositions. 

290. By the Conversion of Propositions we change 
Conversion. thc rclativc placc of Subject and Predicate, 
as from A is B to B is A. 

291. In the Conversion of Propositions, the first form 
Exposita and wc Call ExDOsita. and the second the Con- 

Converse. -^ •' 



n.] OF PEOPOSITIONS. SECT. X. 75 

292. The fundameiital canon which governs the 
Conversion of Propositions is this : Fundamental canon. 

]!fo term ^nay he distributed in the Converse which 
was not distributed in tJ^ Exposita, 

293. As E and I are alike in reference to the distri- 
bution of their terms, one distributing both conversion of 
and the other distributing neither — their ^andi. 
conversion takes place in the same way ; that is, sim- 
ply, No A is B, therefore No B is A. Some A is B, 
therefore Some B is A. 

Exjposita^ No quadrupeds have wings, therefore 
Converse^ No winged animals are quadrupeds. 
Ex])osita^ Some Poets are Americans, therefore 
Converse^ Some Americans are Poets. 

294. This is called Simple Conversion^ and hence 
the Rule, when both Subject and Predicate gi^pie con- 
are distributed, and when neither are dis- version. 
tributed the Proposition may be converted simply. 

295. But in A the Subject and not the Predicate is 
distributed. Hence we cannot convert sim- c9nversionby 
ply if we say, " all American citizens are li^^^^ation. 
free," we cannot say that therefore " all freemen are 
American citizens." We must limit the subject and 
say, therefore " some freemen are American citi- 



zens." 



296. Tliis is called conversion ly limitation or per 
accidens, 

297. A, however, when stated by contra-position, 
may be converted simply. Thus All A is B, ^ by contra- 
No A is non-B, therefore No non-B is A. E^'^^'^convenld 
If the whole of A is in the sphere of B, ^^^p^^- 
nothing which is not in B can a fortiori be in the 
sphere of A. 

298. O, cannot be converted except by first chang- 
ing its quality. This w^e m ay do by connect- conversion of 
ing the Negative with the Predicate by ^• 
which we permute it into I. And then of course it 
may be converted simply. Thus " Some A is not B, 
therefore Some Not-B is A." 



76 LOGia — PART I. [chap. 

Exjposita^ Some brave men are not soldiers, 
Converse^ Some not-soldiers are brave men. 

299. Hence we may convert E and I simply. A by 
limitation, or jper accidens^ an particularly^ and O by 
permutation into I and then simply. 

300. In consequence of the laws of Conversion we 
Immediate In- havc from auv Exposita, its converse as an 

ference by Con- t t . t /• 

version. immediate inierence. 



IV. Of the Substitution of Tekms. 

301. In every categorical Affirmative Proposition we 
Substitution of may always substitute for the Predicate any 

Predicates in.*^ i»iii •! t 

Affirmatives. tcTin wnicH uenotes a wider and compre- 
hending sphere and the Proposition will remain true, 
but it will cease to be- the whole truth. In the same 
Substitution of ^^^J w^ ^^y substitute for the subject any 
the Subject. term which denotes a narrower and compre- 
hended sphere, and with the same effect upon the Propo- 
sition it will still be true, but not the whole truth that 
was contained in the Proposition before the change 
was made. Thus, if A B is " a negro," he is " a man," 
" an animal," " a created being," &c. Or if we say, 
" men are mortal," we may say '' Caucasians are mor- 
tal," " Americans are mortal," " Yankees are mortal," 
" Bostonians are mortal," &c. 

302. By such change Propositions are said to be- 
come more general or more indefinite ; they are true 
but not the whole truth. 

303. In Negative Propositions, in consequence of 
Substitution of the fact that the Predicate is distributed, we 

Negatite^s^. *" may substitute in the Predicate terms in the 
inverse order ; that is, for any comprehensive term we 
may substitute any one of its included spheres. Thus 
A B is not a man, therefore he is not a Negro. If 
Victoria is not a sovereign she is not Queen of Eng- 
land. 

304. But we may not substitute Predicates in the 



n.] OF PROPOSITIONS. SECT. XI. 77 

inverse order in either case ; that is, not a narrower 
for a more comprehensive in Affirmatives, . no substitutes 
nor a more comprehensive for a narrower JTrdel?^ '"''^'^® 
in Negatives. This would be in either case asserting 
something more than the truth."^ 

305. By these substitutions new Propositions are 
made, the truth of which depends upon that immediate in- 
of the Propositions for whose terms the new sufutfon.^^^"^^' 
ones are introduced. Hence the new Propositions 
must be true (though inadequate), by Immediate In- 
ference. 

SECTION XI. 
Of Complex Projpositions, 

306. A Categorical Proposition is called simple 
when its two terms are expressed by single ^simple and 
words. But when several words are re- poTtfons. 
quired to express the cognition the term is called 
Complex. • 

307. It is evident that any substantive, or other 
word which is the name of a thing, a pro- Necessity for 
perty, an action, or a series of actions, may complex terms. 
be a term, as "man," "whiteness," a "step," "walk- 
ing," " to err." And if any language were copious 
enough to affi)rd a name for every possible conception 
which we might ever wish to express, as either the 
subject or the predicate in our judgments, we should 

* It may be well to give a diagram illustrating the preceding para- 
graph. 

Thus let S and P be any two circles or spheres. S included /^i^^^^NP 
in P — this represents the affirmative Proposition S is P. It is ( ( S ) ) 
manifest that any sphere comprehending P must comprehend xl^:^/' 
S also. Let S be Negro, P be Man, and we have " Negroes 
are Men." But let a circle drawn around P denote " animal," so that all 
men are animals, then will it include S also, and we shall have " Negroes 
are animals." 

But in case of the Negative Proposition the Subject is ^—^ ^^-^ 
not included in the Predicate, and we have two circles S and ( ^ ) ( ^ ) 
P, having no point in common. S is not P, consequently S ^— ^ 
cannot be in any narrower sphere which is included in P, or any part of it. 



78 LOGIC. PAKT I. [chap. 

never need to use any other words to express our 
meaning than these simple terms. But such is not the 
case and never can be the case with any human lan- 
guage. 

308. In most cases also when the predicate denotes 
a property which is not one of the differentia of a spe- 
cies, we wish to use in the subject not merely the specific 
term but also the term denoting the genus under which 
the species is included. Thus if we say, " Men who walk 
by faith place a light estimate upon the mere vanities 
of worldly splendor," we give first in the subject the 
genus " men," and then the species " who walk by 
faith." It is obvious that we do not intend to affirm 
the predicate of the whole genus denoted by the 
term " man," but only of one species of men, whose 
differentia is that they " walk by faith." 

309. A simple term, as " man," thus limited be- 
Modais. comes a complex term ; and the words limit- 
ing or qualifying its meaning or its sphere, are called 

MODALS. • 

310. Modals are either Explicative^ Differential^ 
Exceptional^ Exclusive^ Conditional or Protensive, 

311. Explicative Modals are merely rhetorical. 
Expiicativcs. They amplify the meaning of the term 
itself, as when we say '' "inortal man,^'' Since all men 
are mortal the adjective adds nothing either to the 
matter or the sphere of the conception for which the 
term '' man " stands, however much it may add to the 
rhetorical effect of its utterance. 

312. Differential Modals limit the sphere of the 
Differential. conccptiou dcuotcd by the absolute or sim- 
ple term. In that case the term is really the species, 
as the Differential Modal furnishes the Differentia of 
the contained species. Thus " white men, " — here 
'' men " is the simple term, '' white " the modal ; and 
" white men," the complex term, is but a species of 
the genus ••' man " denoted by the differential " white." 

313. While Differential Modals indicate the part 
of the Proximate Genus, which is included in the scope 



n.] OF PKOPOsrrioNs. — sect. xi. 79 

of the judgment, we have another class of modals 
called Exceptionals^ which indicate the part Exceptionais. 
which is not included in the scope of the judgment. 
As " all except the Apostles were scattered abroad." 
Instead of giving the differentia of that portion of the 
Proximate genus which is included in the Predicate, 
it gives the differentia of the part which is not in- 
cluded. Hence the Differential and the Exceptional 
modals are in a sense counterparts and complements 
of each other. 

314. The Exclusive Modals are those which show 
that the predicate can have no other subject Exclusive, 
than that of which it is predicated in the judgment. 
As " Virtue is the only thing worth living for." Here 
virtue is declared to be worth living for. But by the 
modal every thing except virtue is excluded from the 
sphere of the conception denoted by the matter " worth 
living for." Hence of neCessity Exclusive modals dis- 
tribute the Predicate. 

315. Conditional Modals express some separable 
mode or condition of the object represented conditional. 
by the term, so that the object is included in the scope 
of the judgment only while it is subject to that condi- 
tion. Thus " drowning men catch at straws ; " that is, 
" men in the condition of drowning." It does not ap- 
ply the predicate to any species of men at all times 
and under all conditions as the Differential modal does, 
but it makes it applicable to all men when they are in 
the specified condition. 

316. Protensive Modals limit the inclusion of the 
term within the scope of the judgment in protensive. 
reference to time. Thus " the weather is excessively 
cold in winter^"^ — " our plans will sometimes fail," — 
'• testimony sometimes deceives us." 

117. The Protensive Modal neither makes nor im- 
plies any change in the properties of the term, but only 
refers to the time when the object denoted by the term 
is included in the scope of the judgment. This it may 
do defmitely^ as "in winter ; " or indefinitely^ as '' some- 



80 LOGIC. — PART I. [chap. 

times ; " instantly^ as " now ; " or absolutely^ as " al- 
ways." 

318. There is another kind of adjective phrase that 
has sometimes been regarded as a modal, which how- 
ever I have preferred to regard as constituting a com- 
pound Copulative Categoric Proposition (see 322), — as 
''' JE[ar)iilton^ the greatest statesman of his age^^ or "who 
was the greatest statesman^'^ (fee, '^ was a FederalistP 
But the words marked in italics do not constitute a 
modal of " Hamilton," they are the Predicate of a 
judgment to which ''Hamilton" is subject, and the 
Proposition expresses the two entirely distinct and in- 
dependent judgments, that " Hamilton was the greatest 
statesman," &c., and that " he was a Federalist." 

SECTION xn. 
Of Gomjpound Projpositions. 

319. Any Proposition which has more than two 
distinct terms is called a Compound Proposition, and 

Compound coiitalus cithcr expressly or impliedly more 
Propositions, j^^iii oue judgmcut. If it has but two terms, 
whether simple or complex, the Proposition is simjple. 

320. Compound Propositions are usually divided 
into Exjpress and Invplied. They are called Express 

Express and whcu two OT moTC judgmcuts are expressed 
Implied. jj^ ^]^g same Proposition, and Implied when 

one only is expressed and the other is implied. 

The Compound Express Propositions are either 
Copulative^ Causal^ Discretive^ Conditional^ or Dis- 
junctive, 

321. In the Copulative Propositions either the Sub- 
copuiative. jcct or the Predicate, or both^ consist of two 
or more terms connected by a conjunction. Thus A 
and B are C ; A is B and C ; A and B are C and D. 
" Life and Death are both before us ; '' — " Bacon was 
both a philosopher and a statesman." 

322. Sometimes the conjunction is omitted entirely, 
as "Hamilton the greatest statesman of his age yvRS a 



U.] OF PROPOSITIONS. — SECT. XH. 81 

Federalist." And again its place is supplied by the 
relative pronoun and the verb, as " Hamilton who was 
the greatest statesman, &c., was a Federalist." 

323. Copulative Propositions can be resolved into 
simple ones according to the number of sim- Resolved in 
pie judgments contained in them. Thus in St ^'''''''''' 
the example, " Bacon was a philosopher and states- 
man," we have — Bacon was a philosopher, 

" " a statesman ; 
or in the other example given, we have the following : 
Life is before us. 
Death " " " 

324. Or the connective may be a disjunctive con- 
junction, as " Neither wealth nor friends Disjunctively 
can free the body from its pains, nor the connected. 
mind from its fears ; " — and we have, * 

Wealth cannot free -I Jj^^ ^".^y, J"^^ f ^°' 

I the mind irom tears. 

Friends cannot free \ *^^ ^^.*^^ J"^^^ f ^°' 

( the mind irom fears. 

325. It is of course quite possible that one of the 
judgments in a compound copulative will be true, and 
the other or others be untrue. And advan- 

. . {>. .1 /» i 1 • p V /■• j^i Pure and falso 

tage IS oiten tai^en ot this tact tor the pur- judgments com- 
pose of introducing and gaining assent to a 
•judgment which is untrue, by ascribing to a subject 
two predicates, one true and the other false. 

326. Compound Propositions are called Causal when 
one of the judgments assigns the cause or causai. 

sign of the truth of the other. " Christians are happy 
lecause they have obtained the favor of God ; " — " The 
evil are exalted that they may fall ; " — '' Christ came 
to save the world / " that is, '' Christ came [first judg- 
ment] that he might save the world," [the final cause 
or object for w^hich He came into the world.] 

327. Compound Propositions are called Discretives 
whern they contain two judgments in oppo- Discretives. 
site qualities. Thus/' A is B, but it is not D. "A 
and not B is C." '^ A is B but C is not D." " Fortune 

4* 



82 LOGIC. PART I. [chap. 

may take from us our friends but it cannot take our 
honor." " But few men succeed in enrolling their 
names on the list of those who are never to be forgot- 
ten ; " that isj " some men do and some do not suc- 
ceed/' &c. 

328. We have already seen that Conditional and 
Disjunctive Propositions are compounded, implying 
first categorical judgments and then a hypothetical 
relation between those judgments. Hence in one point 
of view they are to be regarded as compounds of cate- 
gorical judgments. 

329. In the compound of the categorical with the 
Conditional. Conditional, the conditional clause is to be 
regarded as a modal. Thus if A is B, C is D ; that is, 
is D {suh modo) A is B. " If the Scriptures come from 
God tliey are entitled to the highest respect." — " The 
Scriptures are entitled to the highest respect on coti- 
dition [conditional modal] that they come from 
God." 

330. So with the Disjunctive, A is either B or C. 
Disjunctive. A is B ou couditiou that it is not C, or 
either A or B is C ; that is, A is C on condition that B 
is not. " The author of this statement is either a fool 
or a knave." He is a knave on condition he is not fool 
enough not to know better. 

331. The more usual form, however, of the com- 
pound categorical with one disjunctive term, is that in 
which one term denotes a logical whole, and the other 
the parts ; as " All men are either Caucasian, Mongol, 
or Negro." 

We shall of course reserve the consideration of the 
judgments which connect the Conditional and Disjunc- 
tive members of these compounds until a subsequent 
place in our treatise. 

832. Of the Compound Implied Propositions two 
only need to be mentioned, the JSxceptives and the 
Exdusives. They each imply a judgment different in 
quality from the one expressed; — this is done by a 
modal. 



n.] OF PROPOSITIONS. SECT. XH. 83 

333. Thus Exceptives while including the expressed 
subject in the sphere of the predicate, make an excep- 
tion of some of the individuals included in Exceptives. 
the implied subject, which consequently are excluded 
from it. Thus " All hut the Apostles fled^'^ implies 
that there were some who were not Apostles that did 
flee. 

334. In this case the expressed judgment is affirma- 
tive and the implied is negative. But if we say, 
" None hut the Apostles remained^^^ we have the nega- 
tive judgment expressed, '' None ; " that is, " no Chris- 
tians remained," — and the implied affirmative judg- 
ment, " the Apostles did remain." 

335. The Exclusive Propositions, while including a 
subject in any predicate, exclude by an im- excIusIvos. 
plied negative judgment all other subjects from that 
predicate, as " Virtue is the only thing worth living 
for." This is precisely the same as the Exceptive in 
which the negative judgment is expressed, as "Nothing 
but virtue is worth living for." 

336. The article 'Hhe^'^ before the Predicate of an 
Affirmative judgment constitutes it an Exclusive, by 
making the Predicate a definite and distributed term. 
Thus " Christ is the Saviour of the world ; " this im- 
plies that He is the only Saviour. 

337. In the conversion of complex and compound 
Propositions they must, as a general thing, be first re- 
solved into simple incomplex propositions, and per- 
muted and converted according to the rules already 
laid down. In one or two cases, however, there are 
facts in regard to their conversion worth noticing. 

338. Exceptionals and Exclusives are easily con- 
verted into each other. '' All but the Apostles fled ; " 
becomes by substituting the exclusive instead ^^^^ ^.^^^^ 
of the exceptional modal, and changing the and^Exdusives 
quality of the Proposition, " The Apostles ''°"''^' ' 
alone did not flee." The same thing would be accom- 
plished with the antithetic Predicate without changing 
the quality of the copula, as the Apostles alone re- 



84 LOGIC. PAKT I.* [chap. 

mained, i. e., did not flee. " Virtue is the only thing 
worth living for," is converted into an exceptional by 
substituting for the subject " nothing," and the ex- 
ceptional modal before the subject, as "Nothing except 
virtue is worth living for." 

339. Any Compound Proposition, whether Express 
or Implied, may always be regarded for the purposes 

Compound ^^ Dcductiou as a simple Complex Proposi- 
Sie tocom". tion. Thus the Copulative '' A and B are C." 
piex. ^ ^^^5 modo^ that is, on condition it is joined 

to B) is C. For the Causal take " A is B because it is C." 
A {suh modo^ that is, because it is C) is B. For the 
Discretive " A is B but not C." A {sub modo, that is, 
on condition it is not C) is B. The same is obvious, 
too, with regard to the Exclusives and Exceptionals ; 
the exclusive and exceptional phrases may be made or 
regarded as merely a modal of one of the terms. 

340. But we may carry this matter one step further, 
and regard the Complex as a Simple Categorical so far 

Complex to ^s thc purposcs of dcductiou are concerned. 
Simple. j^ depends very much upon the fulness of a 

language, whether a conception shall be expressed by 
a single term or not. If we have no single term for it, 
we must use several, and give either its description or 
its definition instead of the term itself And all tlie 
words which Logic requires in the expression of judg- 
ments, are either the copula or the terms ; or instead 
of terms, their definitions or descriptions. Hence what- 
ever words are necessary to express any cognition, 
become but a complex term for that cognition, and it 
is merely accidental for all logical purposes, whether a 
term be expressed by one word or by many. 



SECTION XIII. 

Of Co'iTvparativG Judgments. 

341. Comparative Judgments do not include the 
subject in the sphere of the Predicate. 



n.] OF PROPOSITIONS. SECT. XIII. 85 

342. In Comparisons there are three terms and two 
implied categorical judgments ; as '' A is . Three Terms 
wiser than B." Here we manifestly have iufiSt?^'''® 
the two judgments, A is wise and B is wiser. And we 
have three terms, A the Subject, B the Predicate, and 
the Comparative term, which in this case is " wise.'^'' 
The Predicate is assumed as the Standard The positive 
or Positive term, and the Subject is com- pared Terms!" 
pared with it and is the Coriipared term. 

343. Of Comparative Judgments there may be 
reckoned seven kinds: 1. Comparatives of Different kinds 
simple Intensity. 2. Comparatives of Inten- ""^^"^"^^^^^^^^ 
sity considered as a Cause, 3. Comparatives of Time. 
4. Of Place. 5. Of Manner. 6. Of Means or Method. 
7. Of Patio or Relation. 

344. We may have comparisons in Intensity of 
three varieties : (1) of Equality ; (2) the Indefinite ; 
(3) Comparisons of Inequality; ^^ 

(1.) In Comparisons of Equality the Positive and 
Compared terms are affirmed to be equal in comparisons 
the intensity of the term of Comparison ; of Equality. 
as A is equal to B, in which it is also implied that 
B is equal to A, or that A and B are equal in the 
intensity of that in respect to which they are com- 
pared. 

(2.) In the Indefinite we have the Compared term 
declared to be of as great an intensity as the indefinite. 
Positive ; as " A is as great as B," or " A is as wise 
as B." In these judgments it does not appear that B 
is not wiser than A, &c. 

(3.) In Comparatives of Inequality the term of com- 
parison is used in the comparative degree, inequality, 
and a difference in degree of intensity is declared to 
exist between the Positive and the Compared terms ; 
thus A is greater than B, or A is less than B. 

345. Comparatives of Inequality differ in their in- 
tensity, by being on the different sides of the Difference of 
positive degree, and are accordingly called in^^nsity. 
comparisons of greater or of less intensity. 



86 LOGIC. PAET I. [chap. 

?A6, Comparisons are said to be of greater intensity 
Greater inten- when the Term of Comparison is affirmed to 
belong to the Compared in greater intensity 
than to the Positive, and Comparisons of less inten- 
Less Intensity, sitj when the Term of Comparison is affirmed 
of the Compared in a less intensity. Thus A is greater 
than B, is a comparison of greater intensity — A is less 
than B, is one of less intensity. 

347. We may have Comparatives in which the in- 
intensityasa tcnsity of thc comparatlvc term is considered 

Cause. g^g ^ Cause. Thus, " The weather is so cold 

that the water freezes." 

348. For a comparison of Time we say that " A 
Of Time. occurs wlicn B occurs;" as "It lightens 
when it thunders." 

349. For a comparison in Place we say, "A is where 
Of Place. B is." — " Where two or three are gathered 
together in My name, there am I in their midst." 

350. For a comparison of Manner we say, " A is 
Of Manner. likc B." — " Thc Boy walks like his Father." 

351. We have also a comparative of Method or 
Of Method and Mcaus, as " Hc camc as he went ; " in which 

case the " as " comparative may refer to 
either the means used or to the way by which the act 
was performed. 

352. Then we have Ratios, or comparisons of value. 
Of Ratio. in which one term varies as the other. Thus 
" A is to B as C is to D.— '' The Mercury in the Ther- 
mometer rises and falls as the weather grows warmer 
or colder." 

353. In comparisons of Inequality conversion may 
Conversion of bc effcctcd by cliauge of the intensity to its 

Comparatives, ^pp^gj^^^ Tlius '' A is gveateT than B," — 

'' B is less than A." 

354. But in the Indefinite no conversion can be 
Indefinites con- effcctcd ; wc Say, " A is as great as B." 
no e convert- -g^^ ^^^ judgment Icavcs it possible for A to 
be greater than B, and the mind is uncertain whether 
it is or not. Hence B may be either equal to A, or less 



n.] OF PROPOSITIONS. SECT. XIV. 87 

than A ; and the judgment does not furnish the means 
for determining which it is. 

355. Comparatives in which the Intensity is re- 
garded as a Cause, are converted into Causal comparatives 
Categoric Propositions. " It is so cold that caS^'^ '"^ 
the water freezes," becomes " the ^yatev freezes because 
it [the weather] is so cold.'' 

356. All the other forms may be regarded as Com- 
paratives of Equality so far as conversion is concerned, 
and as such may be converted simply, A is equal to B, 
therefore B is equal to A. 

SECTION XIV. 
Of Probcible Judgments, 

357. A Problematical Judgment is one in which it 
is affirmed that the Copula may be affirmative, probable judg- 
But a Probable Judgment is one in which ^^''^^' 
there is given an estimate of the reasons for affirming 
the Copula. 

358. The value of the Probability is always esti- 
mated (if at all) in a fraction of unity or in a Their value, 
ratio ; unity being assumed as the same as a cer- 
tainty. 

359. The value is ascertained by a calculation of 
chances. One reason for believing any Pro- how ascer- 
position which comes into the present class *^®'^- 

to be true, is because we have known it, or some- 
thing like it to hold true. Thus of any given side of a 
die there is a probability that it will fall uppermost 
at any given throw. If a man commits a crime there 
is a probability that he will be detected, based indeed 
upon the means used for his detection ; but estimated 
by the proportion which the times in which similar 
means have been successful in similar cases bear to the 
times in which they have failed. 

360. All the known cases are considered as so 
many Chances,, which are divided into two chances favor- 

1 j^ir*' 11 Ji.1 P 11 ^ble and unfav- 

classes — the favorable and the uniavorable ; orabie. 



88 LOGIC. PART I. [chap. 

and the probability of any affirmative judgment hav- 
ing an individual case for its subject, and the term in- 
cluding the favorable cases for its Predicate being true, 
is determined by the proportion which the favorable 
chances bear to .the unfavorable. Thus a die has six 
sides — at one throw therefore one of the six sides must 
come up : call that the favorable chance, and as there 
are five other sides, no one of which will be up when 
that specific one is uppermost, we may call the unfa- 
vorable chances five. The probability, therefore, of any 
particular side, say the ace^ being up, is one to five, 
or one-sixth of the whole number. 

361. In order to estimate the probability of any 
judgment therefore, we* must have a totaUty of cases. 
This may be the absolute totality including all actual 
and all possible cases of the same kind, or it may be any 

part of that totality which has fallen under 

Absolute and •*■ t . . ^ i i i i 

assumed total- our obscrvatiou, assumed as the representa- 
tive of the whole. For the estimation of the 
probability, it makes no difference which is assumed, 
provided the part taken be an exact representative of 
the whole. Thus suppose the whole to be one thou- 
sand, out of which one hundred have been favorable 
and nine hundred unfavorable, the chances are one to 
nine. Now if we take any part of this totality, say 
one hundred, if it be an exact representative of the 
totality, the chances will be ten to ninety — that is, one 
to nine ; or if we take ten, they will be one to nine still 
as before. 

362. The improbability, which is the probability 
Improbability, that the iudlvidual will be included among 
the unfavorable chances, is of course the complement 
of the probability in the unity of the whole, whether 
absolute or assumed. Thus if the Probability is th?'ee' 
fourths^ the Improbability is one-fourth, 

363. The balance of Probabilities is the difference 
Balance of Pro- bctwecn the two fractions, and is in favor 
bai.ties. of ^i^g probability or the improbability, as 
the one or the other happens to be the largest. 



n.] OF PROPOSITIONS. — SECT. XIV. 89 

364. The Improbability is not however the same as 
the Probability of the opposite. Thus, in 
throwing a penny, the probability of the nouhe^ame'^ 
head side falling up is I, the probability of The opposite re- 
its falling up in two throws is, say f, conse- 
quently the improbability is ^. But the probability that 
the head will fall down, or the tail fall up, one in two, 
is also f instead of |. 

365. Both the Probability and the Improbability 
are sometimes called Antecedent Probability Antecedent 
and Antecedent Improbability, with reference Probability, 
to the fact that they are estimated before or antecedent 
to the special reasons for affirming the judgment in any 
given case. Thus the antecedent improbability of a 
miracle is based upon the uniformity of nature ; that is, 
the numberless instances in which no mira- Effect of differ- 
cle has been wrought. On the other hand, ^"^ totalities. 
it has been claimed that when we consider the special 
occasion on which it is claimed that miracles have 
been wrought, there is an antecedent prohahility in 
their favor ; the difference in the estimates arises from 
the assumption of different totalities of cases or chances. 
In the one case, forgetting the special occasion or pur- 
pose,"^ the absolute totality of historic events and of 
occurrences in nature is assumed. In the other it is 
assumed that the object for which the miracle is al- 
leged to have been wrought, is to constitute the basis 
of an entirely different totality, is the Differentia of a 
much narrower sphere, within which the chances are 
not only much fewer, but are such as to turn the 
balan<^ of the probabilities on to the other side. 

366. In many cases this value can be expressed with 
as much certainty as any categorical judgment what- 
ever. But there are also some objects both Exact estimate 
in logical and in comparative quantity, o^^^iue. 
whose quantity cannot be expressed in terms of dis- 
crete quantity at all. 

* Nodus deo digmis. 



90 LOGIC. — PAET I. [chap. 

367. In most cases, however, our estimate of the value 
of a probability can be only approximate. We judge 

Approximate ^s nearly as we can from what lias fallen 
estimate. under our experience, assumed as a repre- 
sentative of the whole, the proportion of the favorable 
cases to the unfavorable in the absolute whole. 

368. The probability against any judgment or Pro- 
probabnitF and posltiou is Called its ^mprobability ; and the 
nSke^unitV/ probability and the improbability together 
make up a unit or certainty. 

369. Hence if we have either the Probability or the 
Improbability given in a fraction or a ratio, we can 
find the other by subtracting the fraction from unity, 
or by converting the ratio. 

370. But while the improbability can never be 
Improbability morc than the complement of the probability 

thIJ thi com^- in the unity of the lomcal whole, it may often 

plement of the n i '^ ^ ^ J 

Probability. DC ICSS. 

371. It will happen in many cases that we know 
lUustration. of many reasons for believing a proposition, 
and none for disbelieving ; that is, we may know many 
favorable chances and be entirely ignorant whether 
there are really any unfavorable ones or not. Thjis in 
the moral government -of God, it is perfectly certain 
that in many cases sins are punished in this world, 
and perhaps it is not certain that there is any case in 
which they are not punished in this world. Hence 
there is on the supposition a strong probability in favor 
of the opinion, that any particular sin will be punished 
in this world and none whatever against it. 

372. Improbability, therefore, is not the mere want 

Improbability or abscncc of probability or 2:rounds for be- 
not mere want t . Tr» j_ •■! • iX • * a^' Tj. • 

of Probability, licving. JDut it IS Something positive. It is 
based upon and therefore implies positive ground for 
rZ^'i^believing, or believing the contradictory of a pro- 
position. 

373. There may also be an improbability against a 
proj^osition, when there is no probability or nothing in 
its favor ; and for the same reasons as we have just 



n.j OF PROPOSITIONS. SECT. XV. 91 

given for there being in some cases a probability with- 
out any counter improbability. 

374. There may be many cases in which the general 
probability of which we have just been speak- General and 
ing, may be increased or diminished by spe- Im^L 
cial grounds. Thus, in a community where one in ten 
die of any special disease, the probability that any 
particular individual would die with that disease is 
increased or diminished by the peculiarities of his 
constitution, mode of life, &c. The rates of life insur- 
ance are fixed upon the general probability of the 
duration of life. But this probability becomes so much 
diminished by one's being sick or constitutionally dis- 
eased, that Life Insurance Societies refuse insurance in 
such cases. In Marine and Fire Insurances also, the 
rate of insurance is increased above the general rates 
by considerations affecting the probability of loss, aris- 
ing from the special circumstances of the property 
insured. 

SECTION XV. 
Of Conditional Judgments. 

375. Conditional Judgments affirm the reality of 
the Predicate, on the ground of the reality of conditional 
the Subject. But as the Subject and Predi- Judgments. 
cate are not cognitions merely but rather judgments, 
of which the copula of the second is affirmed on the 
ground of the copula of the first, the first judgment 
is called the Antecedent^ and the second Antecedent and 
the Consequent; thus ''If A is B, C is D." consequent. 
Here '' A is B " is Antecedent — " C is D " is Consequent. 

376. The Antecedent and Consequent taken toge- 
ther are called the Members of the Condi- Members oi 
tional ; they are also its Matter. conditional. 

377. In all Conditional Judgments there must be 
at least three terms and two copulas, as in ^hree Terms 
the case just given. There may also be four at least. 
terms, as ''If A is B, C is D." ''If each man may 



92 LOGIC. PAKT I. [chap. 

hold what opinion he chooses without blame, atheism 
itself will be innocent." Here we have the four dis- 
tinct terms, " each man," " hold what opinion he 
chooses," " atheism," and '' innocent." 

378. The ground of affirmation in Conditional Judg- 
sequence. mcuts is Called the Sequence, Thus if we 
have, " If A is B, C is D," we may ask why ? On 
what grounds can we affirm the judgment, " C is D," 
as a consequent of the judgment that " A is B ? " — the 
answer to this question is what is called the Sequence. 

379. For the most part the sequence or ground of 
affinnation is self-evident ; and for this reason it has 

Not always scldom rcccivcd much attention. But we 
sejf-evident. may havc a conditional judgment when there 
is really no sequence ; thus the gardener says, that 
" If he plants any onions in the new of the moon, they 
will fail to have large bottoms ; " the judgment is in 
form a conditional. But still one may fail to see any 
connection between its members. 

380. It becomes necessary, therefore, to consider 
Sequence can the grouuds of affirmation in the Sequence. 

Id'^tfa^cate'- This cau of course always be stated as a 
ment ^"^ ^' Catcgorical Proposition. If one says, " If 
John has a fever he is sick," and we ask why ? — the 
appropriate answer is, " Because all who have fevers 
are sick.i^ 

381. Any Proposition may be an Antecedent upon 
which any Immediate Inference — whether by (1) Op- 
immediate In- positiou of Judgmcuts, or (2) by Oontra- 
ference. positiou, or (3) Conversiou, or (4) Substitu- 
tion — may be affirmed as a Consequent, in accordance 
with laws and principles of Immediate Inference al- 
ready explained. 

382. If the unlike terms are mere synonymes or 
even equipollent, there can hardly be said to be any 

Identity of An- scqucncc, aud yet the Conditional is good. 
tecedents. Tlius ^' If commou salt is good for seasoning 
food, chloride of sodium is good for seasoning food ; '^ 
the sequence in this case is identity of Antecedents. 



n.] OF PROPOSITIONS. SECT. XV. 93 

383. If the Subject is the same in both Members, 
the Predicate of the Consequent may be a 
superior sphere, comprehending the Predi- the consequent 
cate of the Antecedent; and for the same fha";^of'?he An^ 
•reason, if the Predicate is the same in both ^^''*^'^^"^- 
Members, the Subject of the Consequent may be any 
inferior sphere comprehended in the sphere of the Sub- 
ject of Antecedent. Thus as an example of 
the first case, " If the English are Anglo- JSu^^^^^^^ 
Saxons, they are Caucasians." Here " An- i^Hhi^t^of'thl 
glo-Saxons" are assumed as but a species ^"^^''^'^^°^- 
of " Caucasians." As an example of the second take 
the following : " If virtue is expedient, temperance 
is expedient ; " — " temperance " being one species of 
" virtue," or one of the virtues. But in the first case, 
if the Antecedent is negative, the Predicate of the 
Consequent may be any narrower sphere predicated 
negatively; — " If the English are not Caucasians they 
are not Anglo-Saxons." 

384. If the Predicate of the Antecedent be one of 
two or more Correlatives inhering in the when the pre- 
same subject, the Predicate of the Conse- rifathes^TnSihe 
quent may be any other of these Correla- same object, 
tives. Thus, " If an ultimate particle of matter has 
extension, it has divisibility." But if the Correlatives 
do not inhere in the same object, they must correlatives in 
be predicated negatively in one of the mem- ^^st^Tprfdi- 
bers ; thus '' If the man is the master he is fyin'^onl^Mim- 
not the servant." Or in general, if one of ^^^• 

any two Antithetic terms be predicated of any subject 
in the Antecedent, the other may be predicated of it 
negatively in the Consequent, and vice versa. 

385. The Cause of any thing is always in some 
sense the ground of its reality. Under this general 
principle we may have the following classes of Condi- 
tional Judgments with Antecedents expressive of the 
Cause of the Consequent. 

386. Hence if of several contrary terms, having 
analogous spheres, some property be predicated in the 



94: LOGIC— PAET I. [CHAP. 

Antecedent, which is of the essence of the proximate 
genus — that is, the Material Cause — the same term 
Of opposite ^^y be predicated of any contrary term in 
Ma^iriai caise ^hc Oonscqueut, whether that term be a co- 
Sd^fnToth ordinate or the subordinate of any coordi-* 
Members. j^^^^ fQ the subjcct of thc Antecedent. Thus, 
" If vice is voluntary^ virtue is voluntary ; " — ^here 
voluntariness of action is assumed as the Essentia or 
Material Cause of Moral actions, and vice and virtue 
are two coordinate species of Moral actions, each hav- 
ing a Differentia or Formal Cause of its own. And 
we may also have, " If vice is voluntary, temperance 
[one of the virtues] is voluntary." 

387. If the Antecedent affirms the conjunction of the 
Of the conjunc- Efficicut and Occasional Causes, the reality 
ci^nt'lnd^of^- <^f the Effect may be affirmed in the Conse- 
thTin^e^Seiit! qucut ; thus, '' If the spark falls upon the 
be^ a&med""m powdcr it will cxplodc, or an explosion will 
the consequent, ensuc."— " If thc boy takcs cold he will be 
sick." 

388. If the Material Cause is affirmed in the Ante- 
ofthe Material ccdcut, thc substaucc or gcuus may be 
t^ced'eiTtthlEf." affirmed in the Consequent. Thus, " If ex- 
?J?nt'''ma?Te tcusiou cxists matter exists." — "If the mode- 
affirmed. ^^^^ indulgcuce of plcasurcs is right, the 
temperate use of alcoholic drinks is right." 

389. If a Formal Cause be affirmed in the Antece- 
of the Formal dcut tlic Couscqucnt may affirm the species. 

Antecedent.the Tlius, " If thc tcmpcratc usc of alcoholic 
uffirild^n^he stlmulauts bc in accordance with the law of 
temperance and self-denial, it is right." 

390. In cases where the Conditional has four dis- 
compiex 86- tinct tcrms, the sequence becomes complex 

QP double. In this case we may have several 
grounds of affirming the Consequent. 

391. When the Subject of the Antecedent is re- 
Mo'dehiu.el'lf- gardcd as the Cause of the Subject of the 
or'^lubXice XJonsequent^ and the Predicate of the Ante- 
conJJSuent '^"^ ccdcut affirms of its Subject some mode which 



n.] OF PROPOSITIONS. SECT. XV. 95 

is regarded as the Cause of the mode of the Subject of 
the Consequent, it may be predicated of that Subject in 
the Consequent. Thus, " If the Moon is full the tides 
will be high." Here the Moon is regarded as the 
cause of the tides, and the '' fulness " of the Moon as 
the cause of the " highness " of the tides. 

392. Again the Subject of the Antecedent may in- 
clude the Subject of the Consequent, and the subject of An- 
Predicate of the Consequent include that IfelfnLit^t 
of the Antecedent. Thus, "If the English ^Lnt,%nd"the 
belong to the Teutonic branch of the human cJfn'ieJnt'^^^^^^^^ 
family, the Puritans must be Caucasians." SPllfe'^i^nVecl- 
Here "Puritans," Subject of the Conse- ^^"'• 
quent, are regarded as part of " the English^" the Sub- 
ject of the Antecedent — and "Teutons," the Predicate 
of the Antecedent is included in Caucasians, the Pre- 
dicate of the Consequent. 

393. Or again we may have the Subjects of both 
Members contraries to each other regarded subjects in both 
as Formal Causes, and in that case the Pre- S?a1-^s^'ls fo""- 
dicates will be contraries to each other also ; ^^^ causes. 

" If vice produces misery, virtue may be expected to 
produce happiness." 

394. Or we may invert the order and say, " If hap- 
piness results from virtue, misery will result ^nd the re- 
from vice." ^^'^^• 

395. But besides this the Effect though in no sense 
the ground of the reality of the Cause, is of- of the Effect 
ten the sign or ground of our knowledge of Snt^the^^aiky 
the reality of the Cause, and for that reason con^'stq^m ma? 
becomes an Antecedent, upon which we may ^^ affirmed. 
always affirm the reality of the Cause. If the Cause 
be Immanent or Permanent the Antecedent immanent and 
may be affirmed in the present tense or with- causeT^'affiJm- 
out regard to protension. But if it be only fent TenL.^'^* 
a. Transient Cause, as most occasional causes Transient only 
are, its reality can be affirmed in the Conse- »» the past, 
quent only in the past tense. Thus, " If there is day- 
light we may say that the sun shines ; " — but " If there 



96 LOGIC. ^PAKT I. [chap. 

is an explosion, we may say that there has ieen powder 
and fire." — " If there is small pox, we may say that 
the infecting virus has teen communicated to the sys- 
tem." 

396. I have said nothing thus far of the Quantity of 
Quantity and thc Mcmbcrs of thc Conditional. But as the 

Members. ° Antecedent is the ground on which we affirm 
the Consequent, it is evident that no term which has 
not been used as a distributed term in the Antecedent, 
may be used as a distributed term in the Consequent. 
But for the most part terms are regarded as Continuous 
Wholes in Conditional Judgments. 

397. We have also spoken only of simple Catego- 
compiex and ricals as Members of the Conditional. But 

Member" in thcsc Mcmbcrs may be either Complex or 

Conditionals. r^ -y r^ i • ^ ^ ^ 

Compound Categoncals ; and as we have 
before seen the Compound may be regarded as Com- 
plex, and the Complex as simple Categoricals — only 
taking care not to separate or omit any of the parts of 
the Complex term. 

Besides the above modes of compounding the 
Conditional, there are two others which deserve a 
mention. 

398. If we have two or more Antecedents, the Co- 
pulas of which are each independent of the Copulas of 

Compound ^^ othcrs rcspcctively, and one Consequent, 
Conditionals, -j-]^^ Copula of which is affirmed on condition 
of the truth of all the Antecedents, we shall have what 
may be called a Compound Conditional / thus, 

IfAisB) , . J). 
andlfAisCf^'^-^' 
" If the Departed are cognizant of what takes place on 
earth, and if they retain the same feelings towards us 
as they had while they were here, they must sometimes 
be intensely pained by what they see in the course of 
life which we are now pursuing." 

399. Again we may have what is called a Con- 
Continuous tlnuous Conditional in which the Consequent 

Conditionals. ^^ ^\^q gj.g^ bccomcs thc Antecedent to the 



II.] OF PROPOSITIONS. SECT. XVI. 97 

second, and so on. Thus, " If A is B, A is C. If A is 
C, A is D," &c. — " If God is just He will punish the 
wicked. And if He punishes the wicked, surely they 
that blaspheme His Name will be signally con- 
founded." 

SECTION XVI. 

Of the Disjunctive Judgments. 

Disjunctive Judgments have been defined to be 
those in which one of two Categorical Judg- Disjunctive 
ments is affirmed to be true, on the ground Judgments, 
that the other is not true. 

400. This is called the Principle of Excluded Mid- 
dle. It supposes two judgments so related Excluded Mid- 
as that there is no other judgment in the ^^^• 
same matter, differing only in quantity and quality, or 
both, and being in a sense between them. 

401. Thus if we take A and E, we have the subal- 
terns between them ; thus, None between 

All A is B, '^^"^^""^• 

No A is B; 
Now '^Some A is B," is less than "All A is B" 
(in affirmative quantity), and more than " No A is B ; " 
since the latter has no affirmative quantity. In the 
same way " Some A is not B " stands between " No A 
is B," and " All A is B." 

402. Hence either of these Subalterns may be true 
while both the Universals in the same quantity are 
false. 

403. But if we take the Contradictories there is no 
such Middle Proposition ; — " Either All A is Between con- 
B," or " Some A is not B,"— and " Either tradictories. 
No A is B," or " Some A is B." There is no Middle 
Proposition — no other Proposition in the same matter 
which can be true and both of these be false. 

404. The same will hold true of the Sub-contraries 
also. " Some A is B, and Some A is not B." Between sub- 
Now both ipay be true — but there is no contraries. 



98 LOGIC. PART I. [chap. 

Middle Proposition between them ; so that if one be 
false, the other must be true. 

405. Hence in the first place if we have two Pro- 
inference from positious iu thc samc matter, being either 

the oregoing. QQj^^p^^jQ^Qpigg qj. Sub-contrarics, we may 

affirm that one or the other of them is true, and 
consequently we may affirm one of them to be true on 
condition the other is not. 

406. But we may have Disjunctives in matter 
either partly or wholly different ; they all come back, 
however, as we shall see, to the case just stated, of 
either Contradictories or Sub-contraries. It will be 
necessary to investigate this relation a little further. 

407. Since in nearly all cases of Disjunctive Judg- 
ments there is one term common to the members, we 

Coordinate ^^^J ^^U thosc tcrms, whicli are different in 
Terms. each, for the sake of convenience, Coordinate 

Terms. 

408. Any term and its privative being complements 
of each other in the proximate genus, must be contradic- 

positive and torics to cach other in reference to any indi- 
the^prSatS vldual contaiucd in that genus. If then we 
ExciudeTMid" have " A " and " non-A,''— as the two coor- 
'^'^' dinate parts of a whole, — as X, and Z as an 

individual contained in that whole ; then " Z must be 
either A or non-A ; " that is, it must be included in 
one of the parts. But of course the part " non-A " may 
be denoted by a positive term representing a coordinate 
species of X, just as well as by the privative "non-A." 
Hence making this substitution, we may have " Z is 
either A or B." 

409. But again, if instead of Z denoting an indi- 
vidual, we have any term denoting a class compre- 

if the common hcudcd also uudcr X, then in one of the 
leSterm it nicmbcrs of the Disjunctive it must be used 
u.bu\ed%n"one ^^s au Undistributed term. Thus let " man" 
member. ^^^ ^ wliolc, and "free" and "slave" the 

coordinate species ; — ^let "Negro" be also a class com- 
prehended in " man," and we may say either " all 



n.] OF PROPOSITIONS. SECT. XVI. 99 

Negroes are free," or " some Negroes are slaves ; " 
or either " some Negroes are free ; " or " all Negroes 
are slaves." 

410. In the second case we may have a logical 
whole, with a property common to some of ^he two Mem- 
the parts or individuals contained in that pfdinaiTi^^sSb" 
whole. This property we may constitute J®^^^- 
the Differentia of a species, and then divide the whole 
into parts in such a way that this property will be pre- 
dicable of some one part or of some thing contained 
in the whole which is not that part. Thus let " vege- 
tables" be such a whole, and "poisonous^' such a 
property, and " cereals " a class of vegetables, then 
we may say, " Either cereals are poisonous, or some 
[vegetables] not cereals are poisonous." Or again, 
let " substance " be any logical whole, and " matter " 
one kind of substance, and we may say '^ either mat- 
ter, or something which is not matter, is eternal." 
Now suppose that substance which is not matter is 
'' spirit," and we may say, " either matter or spirit is 
eternal." 

411. In this case, as in the precedins;, one of the co- 

/»,T ..T j_ , r"i T ordinate term^3 

one 01 the coordmate terms must be undis- must be undis- 
tributed in case they do not stand for indi- are""^^ genemi 

.-IT *^ terms, 

viduals. 

412. If there are more than two coordinate terms, 
they must be positive terms, and each denote More than two 
its part by differentia of its own. These coordinates. 
parts, how many of them soever there may be, may 
always be reduced to two, by taking any one as posi- 
tive, merging the Differentia of the others, and includ- 
ing them in the privative of the one assumed as positive. 
Thus the coordinate parts, A, B and 0, may be reduced 
to two, as "A" and ''non-A,"— or '*B" and '^non-B," 
in which case " non-A " includes " B and C," — and 
''non-B," ''A" and '^ C." 

413. The Divided Whole may be regarded as a 
logical, or a continuous, or a collective whole, .p^e Divided 
and it may be the absolute whole, or only ^*'^'®- 



100 LOGIC. PART I. [chap. 

some assumed relative whole. When, however, it is 
but a relative whole, some means must be given in the 
Proposition stating the Disjunctive, to fix the mind 
upon the limits of the sphere of the assumed whole. 
Thus, '* A wise lawgiver must either recognize the re- 
wards and punishments of a future state, or appeal to 
a Providence administering them in this." Here the 
assumed whole is " wise lawgiver s^^"^ and it is divided 
into two classes, — (1) those who appeal to rewards, &c., 
in the future life ; and (2) those who refer to a Provi- 
dence administering such rewards and punishments in 
this state of being. 

414. Instead of coordinate terms we may have one 
coordinate and the subordinates of the other, as in the 
Coordinate and followiup; casc : "The earth is either eternal, 

Subordinates oi .-, i «» i A^ ^ c* » . ■% 

its Coordinate, the work 01 chaucc, or the work oi an intel- 
ligent Author." 

Here " the origin of things " is the logical whole. 
The first division, all things either had an origin or 
had none, i. e., " are eternalP But things that had an 
origin (the positive part, with reference to the whole) 
are divisible into two classes ; — (1) those that came by 
chance, and (2) those that had an intelligent Author. 
Hence the Formula above given: " The earth is either 
eternal (had no beginning), or (its beginning) is from 
chance, or from an intelligent Author." 

415. But it is not necessary that the coordinate 
terms should denote coordinate parts of any division. 
The Coordinate They cauuot iudccd be disparate parts, since 
be'oisp'SrWfn thcrc is no necessity that any number of 
the same whole, disparate parts should include all that was 
comprehended in the Divided whole. Privatives, as 
well as Negatives, are always and only coordinates 
of their Positive. But while disparate parts do not 

Alternate spe- ncccssarily include all the individuals of a 
?itlcoordmale Divldcd wholc. Alternate Species do include 
Tunafvi" ju^dg^ them all ; and more than that, they include 
ment. somc of tlicm twice at least. Every indi- 

vidual must be contained in one of a set of coordinate 



n.] OF PKOPOSITIONS. ^SECT. XVI. 101 

species, and can be contained in no more than one. 
In Disparate Species or Parts the same individual may 
be contained indeed in several, but many may not be 
contained in any enumeration of Disparate Parts. But 
in Alternate Species, while no one may be omitted, 
many may be contained in several of the species. 

416. But although the sphere of two Alternate 
Conceptions is the same, the matter is not. The Matter of 
Hence the Differentia of several Alternate ^pf "niS ^/if; 
Species IS likely to have many points m '^°"'^- 
common, and must have some that are not so. Now 
suppose an individual to have a property which we 
know to be a part of the Differentia of one or two Al- 
ternate Species, we can predicate these species of that 
individual disjunctively. Suppose we have a collection, 
consisting of portraits of poets and philosophers alone, 
this collection being one whole — poets and philoso- 
phers would be the Alternate Species, including all 
the individuals in that whole. But they are not Coor- 
dinate Species, since the same man may be both a 
poet and a philosopher, conceived of from different 
points of view. Hence of any one whose portrait we 
know to be in that collection, suppose it to be Cole- 
ridge, we may say, " Coleridge was either a poet or a 
philosopher." 

417. But finally there may be Disjunctives with no 
term common to the members, as, " Either A is B, or 
C is D, or E is F," &c. It is hardly possible Disjunctives 
to enumerate the particular forms and rela- with four terms, 
tions which the terms may assume ; since these judg- 
ments, as in all preceding cases, must be parts of a 
whole, and reducible to an Excluded Middle. We must 
be able to show that there is no judgment except one 
of those enumerated, that will contain the truth which 
the Disjunctive is designed to affirm. 

418. Thus if I wish to account for the diversities in 
the human race, I may say, " Either the}^ sprang from 
different origins," or " the diversities have been pro- 
duced by the influence of climate^ mode of life," &c., — 



102 LOGIC. ^PAET I. [chap. 

or " God must have interposed to produce the variety 
miraculously." Here the divided whole is " the origin 
of the diversities in the human family ; " and if the 
members of the disjunctive enumerate all the parts and 
species to which it can be referred, whether Coordinate 
or Alternate, one of them must be true. If not, there 
must be some other and Middle Judgment which may 
be true. 

419. The Conditionals and the Disjunctives are 
compounded in two ways : 

(1.) A Conditional Antecedent with a Disjunctive 
Compound of ConscQuent, as, '' If A is B, A is either C or 

Conditionals & -,^ ,, c7 Ti? xi ill i i ' • -j. ' 

Disjunctives. D. — " 11 thc world had a begmmng, it is 
either the work of an intelligent Author or the product 
of chance." 

(2.) We may have a Disjunctive Antecedent, thus, 
" If either A is B, or A is C, A is D." This constitutes 
Dilemma. what is callcd the Dilem^ia — " If the patient 
either eats or abstains from food, he will die " (in the 
one case from the effects of the food, in the other from 
want of food). 

420. In stating Dilemmas it is not uncommon to 
omit the Consequent to the Disjunctive Antecedent, as 
being too obvious to need explicit mention. 

421. Since Disjunctive Judgments always affirm 
Disjunctive ouc of thc Mcmbcrs to be true, on condition 

Judgments con- .t . r» ii ,i » n ^ 

verted into Con- that uo ouc 01 the othcrs IS lalse, we may 
always convert the Disjunctive into a Con- 
ditional by contra-position of one Member for an Ante- 
cedent, and using the other or others, if there be more 
than one, as Consequent ; thus, " Either A or B is C," 
therefore " If A is not C, B is C." 



SECTION xvn. 

Of the Grounds of Affirmation. 

422. The grounds upon which judgments are af- 
fiSo^o"/'^^^ firmed are reducible to three ^ — (1) the Prin- 



II.] OF PROPOSITIONS. — SECT. XVII. 103 

ciple of Identity and Contradiction ; (2) Sufficient 
Reason, and (3) Excluded Middle. 

(1.) The first Principle is sometimes spoken of as 
two, as in fact it is. 

(a) Where the terms are synonymous, or the judg- 
ment affirms the identity of the Subject and principle of 
the Predicate. Such is the case in all Defini- identity., 
tions ; thus, a triangle is " a figure with three angles," — 
" a quadruped is an animal with four feet." 

(5) But there are some terms the relation between 
which is so founded in the nature of the ob- principle of 
jects for which they stand, that the relation contradiction, 
cannot be denied without destroying the conception of 
one or the other of these objects. Thus if we say, 
" every effect must have a cause ; " this is not a judg- 
ment of identity, for " effect " and " cause " are not 
the same. But the affirmation depends upon the prin- 
ciple of contradiction ; that is, if we say " here is an 
effect without a cause," we at the same time deny that 
it is an effect. If we say that " this triangle has but 
two sides," we deny that it is " a triangle." 

423. The force of this ground of affirmation is well 
exhibited and tested by resolving the judg- mustration. 
ment into a cognition wdth its modal. 

Thus in the Principle of Identity, we have '^ Vic- 
toria is Queen of England," resolved into a cognition 
or term, it is " Victoria Queen of England." Again, 
a "triangle has three sides," — a "three-sided tri- 
angle." 

424. Or to try the principle of contradiction, " this 
effect has no cause," becomes " a causeless effect ; " — 
" this triangle has two sides only," becomes " a two- 
sided triangle." In each of these cases the term and 
its modal are incompatible, and taken together consti- 
tute an impossibility. 

425. (2.) The second ground of affirmation is called 
sufficient cause or sufficient reason, sufficient reason. 

{a) This ground assumes that there is no sufficient 
ground or reason in the nature of the matter itself. 



104 LOGIC. ^PART I. [chap 

If we say, " the Earth exists," the will of the Creatoi 
Reason of IS Considered as the ground of the reality of 
being. j^g being. If we say, " all bodies gravitate," 

the will of the Creator is again considered the ground 
of the reality of the truth which we affirm. Or if we 
speak of the acts of man, whether past, present, or 
future, his will is considered the sufficient ground of 
the reality of these acts, the ratio essendi. 

(h) The means by which we know the reality, the 
ratio cognoscendi, may and generally are in fact quite 
Reason of different from the ground of the reality itself, 
knowing. Take the reality of gravitation, for instance, 
the ground of the reality is the will of God ; but our 
means of knowing the reality are experience and ob- 
servation. The reality of the Positive Institutions of 
Christianity depends upon the will of God for its 
ground, but one means of knowing that reality is Reve- 
lation. 

426. (3.) The third ground of Affirmation is called 
Excluded Middle, thc Excludcd Middle. 

Between any Judgment and its Contradictory there 
is no Middle or Third Judgment. 

Hence in any case if we prove the falsity of one 
judgment, this becomes the ground for affirming its 
contradictory. 

427. But there is especially one class of Judgments 
which can be affirmed on no other ground than that of 
Excluded Middle. 

428. Such is the case with all affirmative Proposi- 
Affirmatives tious witli ucgativc Prcdicatcs, and all in 

predica^tlt.""^ wliicli tlic Predicate denotes infinity. 

429. In proving a Proposition with an affirmative 
Copula, we include the Subject in the sphere of the 

Proof of Nega- Predicate, and this we do by showing that 
lives. ^i^Q Subject has the Essentia denoted by the 

Predicate. But if the Predicate be negative, it is de- 
noted by no matter of its own ; and we can include 
the Subject in the sphere of a negative Predicate only, 
by showing that it does not contain the Essentia of its 



n.] OF PROPOSITIONS. SECT. XVII. 105 

Positive. That is, we disprove the Proposition with 
the positive Predicate (A is B), and infer by Excluded 
Middle its contradictory that " A is non-B," which is 
at once resolved into " A is not B." 

430. So also if the Predicate is infinite, as " space 
is infinite ; " we can afiirm or prove our own p^oof ^f ^^^, 
judgment only on the ground of the falsity "^^^^• 
of the contradictory, and by the principle of Excluded 
Middle.^ God, Eternity, and Space can have no bounds, 
therefore they are infinite. 

* I do not propose here to touch the question between Sir William 
Hamilton and Schelling and Cousin, with regard to our direct cognition of 
the infinite and unconditioned. I am not speaking of cognition but of proof; 
the former in their phrase is the function of the Reason, the latter of the Un- 
derstanding. 



5* 



106 LOGIC. — PART I. [chap 



CHAPTER in. 

OF SYLLOGISMS. 



SECTION I. 

Classification of Syllogisms. 

431. A Judgment is called Intuitive when the mind 
Intuitive judg- perceives and affirms the relation between 

menis. ^^q cognitions when they are brought toge- 

ther in consciousness, without the intervention or aid 
of any other cognition. 

432. But it is not always the case that when two 
cognitions are thus brought together in the conscious- 
Limits to In- ness, the mind affirms or denies any kind of 

tuition. agreement intuitively. It may be at a loss 

or in doubt. This doubt or inability to see the relation 
must be the result of the limited nature of our faculties. 
No such doubt or hesitation can be felt by an omni- 
scient mind. 

433. If now we have two cognitions, A and B, and 
cannot see the relation between them, so as to consti- 

Deductive ^^^^ them into a judgment intuitively, we 
judgaients. j^^j g^^ j-j^^ Tclation bctw^ecn each one of 
them,- and a third term, as C for instance. We may 
see that " A " is C, and that C is "B," and fi-om these 
two intuitive judgments we may have the judgment A 
is B, which in that case is called a Deductive Judg- 
ment. 



ni.] OF SYLLOGISMS. SECT. I. 107 

434. Thus all deductive judgments, which in fact 
make up the great mass of human knowledge Deductive 
and science, are based upon intuitive judg- ed'^u™on"1n't!a'- 
ments as their premises, and may be resolved ^'''^■ 
back into such intuitive judgments. 

435. The term which is thus brought in as the 
means of forming the two judgments is called the 
Middle Term. And when there is but one Middle Terms. 
Middle term, the conclusion A is B is a Deductive judg- 
ment of the first degree, or but one step removed from 
the Intuitive. If, however, two such Deductive judg- 
ments become Premises to a Conclusion still further 
removed, there will have been more than one Middle 
term and more than two Intuitive judgments. The 
Deductive judgments, however, differ from each other 
only in the degree of remoteness from the primary In- 
tuitive judgments, which constituted the first elements 
in their deduction. 

436. The Deductive Judgment or Conclusion is 
never contained in or derived from one of the Mediate infer- 
Premises alone by any process of Imme- ^"^^• 
diate Inference. But it is deduced from the two Pre- 
mises by means of the Middle term, and is therefore a 
Mediate Inference. 

437. By Syllogism we mean any combination of 
two judgments as Premises in such a way as syiiogism de- 
that a third, different in matter from either ^"^'^• 

of them taken separately, results. The judgment so re- 
sulting is called the Conclusion. 

438. Syllogisms are of three kinds ; Categorical, 
Conditional, and Disjunctive. They are syiiogisms di- 
Categorieal when all the Premises are Cate- classes. 
gorical ; Conditional when one Premise is Conditional ; 
and if one Premise is Disjunctive^ we call the syllo- 
gisms Disjunctive. 

439. But Categorical Syllogisms are still further 
susceptible of division, according as the categorical 
Premises may be either purely Categoric, vfjef 'ISo v^^ 
Comparative, or Probable Judgments. "^^>^^- 



108 LOGIC. PAKT I. [chap. 

440. In the pure Categorical Syllogism there are 
Pure catego- three Propositioiis, two Premises, and a Con- 

> ogisms. ^^^gj^j-^^ ^^^ three distinct Terms. 

441. Of these Terms in the simplest and most natu- 
Relation of ral Formula (Barbara), one, as individual 

Terms in the -, • • • i i i • ^i i 

Premises and or sub-SDCCies, IS incluQea m the second as 

in the Conclu- . ^ Ji xl j.i • j • • i i i 

sion. a species, and then this second is included 

in the third as the Genus— in the Premises; and 
thus in the Conclusion the first is included in the 
third. 

442. Hence the first, as its sphere is the narrowest, 
is called the Minor term ; and the third, as its sphere 

Names of the ^^ the largcst or most comprehensive, is 
Terms. callcd the Majoe term ; the other is called 

the Middle term. The Minor and the Major terms 
together are called the Extremes. 

443. But this order is not always observed ; and as 
in some syllogisms it is impossible to determine which 

Local, Minor, tcrm has the widest sphere, a more artificial 

Middle, and i • ^' • • i j^i j^ r» t 

Major Terms, denomination IS given to the terms lor ordi- 
nary purposes, by which the Predicate of the Con- 
clusion is called the Major term, and the Subject of the 
Conclusion the Minor i^Yxn, 

444. Hence the Nominal Minor Term, w^hether the 
real minor or not, is the real subject of the Syllogism; 
and the Nominal Major is the real Predicate of the 
Syllogism, and the Syllogism is made for the purpose 
of proving the Major term as Predicate of the Minor 
as its subject. 

445. From this denomination of the Terms in a 
Syllogism the names of the Premises are derived. As 

Names of the ^^^ tcrm uiust appear in two Propositions, 
Premises. ^^^ ^g ^^ Miuor aud thc Major appear in 
the Conclusion, the Middle term must be found in 
each of the Premises. The other term in each Pre- 
mise must therefore be either the Minor or the Major, 
and hence the Premise is called the Minor or Major 
Premise, according as it contains the one or the other 
of the extremes. 



in.] OF SYLLOGISMS. — SECT. II. 109 

Thus S is M, 

" M is P, 

" Sis P. 
Here " S is M " is the Minor Premise, " M is P " is 
the Major Premise, and "S" and "M" are the Ex- 
tremes. 

446. It is usual in stating Formula to state the 
Major Premise first. In popular language, when we 
are speaking of an argument, it is usual to » Principle " 
call the Major Premise ^^ the PrinGvpW^ & "instance." 
upon which one argues ; and the Minor Term " the 
Case^^ or " the Instance^'^ or " the Exam^le^'^ coming 
under it. 

447. The Conclusion until it is considered as proved, 
that is until satisfactory Premises have been assigned, 
is called ^' the Qiiestion^'^ and is considered Question. 
as yet sub questione^ or under inquiry. 

448. As a Question it may be stated in two forms, 
What is S? AndisS.Pf 

449. In the former case we are supposed not to 
know what is the Mai or term ; or in other Question as 

J J J. 1 j.1. • X to the Major 

words, we do not know the proximate genus Term, 
to which it belongs, and consequently we are said to 
be in doubt about the Predicate, and the Question is 
concerning the Predicate. 

450. When the Question is in the other form, " Is 
S, P?" we have both terms given, and are Question of 
said to be in doubt about the Copula — or the *^® ^^vmi^. 
question is said to be concerning the Copula — not what 
is the Predicate, but whether it may be affirmed of the 
Subject or not. 

451. If the Question be concerning the Copula it is 
answered by some one of the Formula, which Questions of 
we are about analyzing. But if it be con- {["edb^FSimufl; 
cerning the Major term, it can be answered Questions of 
only by means of some one or other of the intwS'S^^'I? 
Methods of Investigation, treated of below, ^estigation. 
(Part n. Chap. U.) 

452. In Categoric Formula the question concerning 



110 LOGIC. PART I. [chap. 

the Copula is determined by means of the Middle term. 
Office of the which for this purpose is used in four differ- 
Middie Term, q^^ wajs I — (1) Whcu the Copula is expres- 
sive of the identity of the terms in either or both the 
Premises ; (2) when it expresses a relation in Logical 
Four ways. Quantity; (3) when one or both Premises 
are Comparative ; (i) when one or both are Probable 
judgments. 

SECTION n. 
Of Pure Categorical Syllogisms. 

I. Of the Fiotjee of the Syllogism. 

453. We have already remarked that the Middle 
term by position is not always the Middle in Logical 
Quantity between the two extremes, and its office and 
effect depends very much upon its position. These 
different positions which it may occupy are four in 
Figures. Humber, and are called the Four FiorRES, 
as follows : 

1st. 2d. 3d. 4th. 

Mis P. PisM. Mis P. PisM. 

SisM. SisM. MisS. MisS. 

S is P. S is P. S is P. S is P. 

454. The Differentia of these Figures may be thus 
stated : 

In the First Figure the Middle term is Subject of 
Differentia of thc Maior Prcmisc, and Predicate of the 

the Figures. -.--• 

Minor. 
In the Second, it is Predicate in both Premises. 
" Third, it is Subject in both. 
" Fourth, it is Predicate of the Major and Sub- 
ject of the Minor. 

455. From this it appears that the Fourth Figure is 
only the inverse of the First. 

456. This Fourth Figure has been objected to on 
Fourth Figure tlic grouud that it is unnatural, and one 

oject« to. j^nrainst which the mind rebels. On the 



in.] OF SYLLOGISMS. SECT. II. Ill 

other hand Professor De Morgan thinks it the most 
natural of any. 

457. But such considerations or arguments are of 
no force. The question is not what is pleas- Answers, 
ing, but what is possible. The Subject or Minor term 
of an argument is generally fixed or determined be- 
yond our control by the circumstances and necessities 
of the case, and we are obliged to take the arguments 
as we find them. 

458. It has been claimed also that there is an 
" Unfigured Syllogism " by Mr. Thompson.^ ^, ^,^^^^^^ 
Thus " Copperas and sulphate of iron are syiiogisms. 
identical — sulphate of iron and sulphate of copper are 
not identical, therefore copperas and sulphate of copper 
are not identical." This he argues is unfigured^ because 
neither term in any one of the Propositions can be called 
either Subject or Predicate. But if a man speaks, he 
must speak of something^ and that is '' the Subject ; " 
he must ^2ij something oJF it^ and that is "the Predi- 
cate." Thus the Proposition, " Copperas and sulphate 
of iron are identical," is precisely tantamount to either 
" copperas is sulphate of iron," or " sulphate of iron 
is copperas;" and either term would become Subject 
or Predicate, just according as the one or the other 
object was the subject of the conversation. 

459. It will be remembered that the Comprehending 
Sphere is always to be predicated of the comprehend- 
Comprehended Sphere in an Affirmative p"lh?nded^**°** 
Proposition. Thus, If A is comprehended '^p^eres. 

in the sphere of B, we have A is B. Consequently 
"A" and "B" have spheres that are coincident to 
the extent of " A's " comprehensiveness ; and all the 
matter included in the conception "B," is ascribed 
to every individual included in the sphere of " A." 

460. Nor do we need to make any exception in 
favor of those Propositions in which the Subject and 

* " Outline of the Laws of Thouglit," p. 253. Thompson, however, is 
but following Sir William Hamilton. 



112 LOGIC. PART I. [chap. 

the Predicate are Identical, or Alternate Conceptions of 
Identical ^^c samc objcct ; as '• common salt is chlo- 
spheres. j.[^q ^f sodium ; " — " Victoria is the Queen 

of England." In this case the spheres of the Subject 
and Predicate are identical, indeed, but still the Sub- 
ject is included in the sphere of the Predicate as truly 
as a man is included in his own skin. 

461. If, however, one sphere is excluded from an- 
other, as " A " from " B," then " B " is the predicate 

One Negative ^^ " A " iu a negative Proposition, and we 
Sphere. }i^YQ " A is uot B ; " and the spheres " A " 

and " B " have no individual common to both. 

462. And if both Premises are Negative they will 
Both Spheres givc US thc thrcc sphcrcs, possibly exclusive 

con^clus'ion. "° of cach othcr, though by no means certainly 
so. Hence we shall have no conclusion. 

463. This may be constructed thus : — /-^ /^ 
Two circles, S and P, exclusive of each v£y \^ 
other ; this is read, " S is not P." Now 
suppose we have another sphere M, and we read, " M 
is not P," or conversely, " P is not M." We know 
from this that P is not in M, nor M in P, but whether 
M is included in S or not, we do not know. It may 
be or it may not for aught that appears. 

464. The First and Fourth Figures being but the 
The Principle couvcrsc of cach othcr, we may construct 

of the First and .i -r»» • i i»iii» 

Fourth Figures. thC PnUCiplC UpOU whlch tllCir /-TvT-.^ 

validity depends, thus three circles as fol- 
lows : — If S is in M it must be in P, and 
some of P must be in S. 

(1.) If now the Middle term is a species compre- 
hending another, as S, and wholly comprehended in 
Affirmative auothcr, as P, then S is comprehended in 
Conclusions, p^ ^^^^ convcrscly some part of P must be 
comprehended in S ; that is, " All S is P," and " Some 
P is S." 

(2.) But if the Middle term comprehends one Ex- 
treme, and is not comprehended in the other, then we 





m.] OF SYLLOGISMS. — SECT. II. 113 

can have only a N^egative Conclusion ; that Negative con- 
is, the Extremes have no part of their spheres an"dTolnif 'Fi- 
coincident. 

(3.) Or suppose that the Middle term is in the 
larger circle and the smaller one is not in the Middle, 
then some part of the larger one must be out of the 
smaller one. 

465. But in the Second Figure the Middle term is 
Predicate in both Premises. s^eSrigife.^ 

This we may construct as follows : — By 
one large circle M, comprehending two 
smaller ones S and P ; — S and P need not 
cut each other, although they may do so. 
They may also both be in M without being 
at all coincident with each other. But the (SJ.dS™n''*1n 
fact of their being both in M proves nothing ^^^^"^ ^^»"'"^- 
with regard to their being coincident. Hence we can 
have no Affirmative Conclusion by necessity. 

466. If, however, either S or P is made coincident 
with M, then of course the other Extreme if the Middle 
cannot be included in M without being in ^^ may ^ha?e 
the other, and we may have an Affirmative ^ <^onciusion. 
Conclusion. 

467. But if either S or P be in M, and the other be 
not in it — that is, if one Premise be negative, S and P 
cannot be coincident, and we shall have a Negative 
Conclusion. 

468. If the Middle term, whether species or indi- 
vidual, is contained in two others, they must be coin- 
cident in part. 

We may construct this by three circles 
drawn as follows : — ^If the small circle M be 
in both the others, they must be coincident in 
part, and have enough in common to include 
M at least. 

This explains the validity of the Affirmative Syllo- 
gisms in the Third Figure. But if the Mid- pr;,eipioofthe 
die term be wholly excluded from one of the ^^"^ ^'^'''^' 
circles, that part of the other in which it is contained 




114: LOGIC. — PAKT I. [chap. 

must be excluded from it also. But the Middle term 
must be excluded as a whole from one of the circles, 
or else they may be entirely coincident, and a part of 
No Universal ^ bc cxcludcd from both. Hence we have 
S'e"''Thi?d Fi? ^iily Particular Conclusions in the Third 
gure. Figure. 

469. It is also necessary that the Middle term be 
once distributed in the Premises. For 

(1.) In the First and Third Figures, when it is Sub- 
ject in the Major Premise, if it be not included as a 
whole in the Major term, or excluded as a whole, the 
Minor term may be included in the Middle without 
being included in the Major term, if the Premise is 
affirmative, or being excluded from it if it be negative. 

(2.) In the Second Figure, as we have seen, one 
Premise must be negative, and consequently the Mid- 
dle term will be distributed as Predicate of a Negative 
Premise. Or if either S or P become coincident with 
M, and we have an Affirmative Conclusion, it is be- 
cause in that case M or the Middle term becomes 
distributed ; and in the Fourth Figure the same rea- 
soning applies as to the First, only taken in the inverse 
order. 

470. It appears from the foregoing demonstrations. 
Undistributed that tlic Middle term must be once distri- 
buted ; that is, taken as a whole in one of 

the Premises. Otherwise we have the fallacy in 
Form which is called Vndistribitted Middle, 

As an illustration of this Fallacy take the follow- 
ing : 

" Moral virtues are habits. 

Skill in the mechanic arts is a habit. 
.-. Skill in the mechanic arts is a virtue." 
Both Premises in this Syllogism are true. But 
there are " hahits " of at least two different kinds — 
moral virtues being habits of one kind, and skill in the 
mechanic arts habits of another kind. And since the 
term '' Jidbits^'' being the Middle term, is -not distri- 
buted, the Major term is compared with one part of 



m.] OF SYLLOGISMS. SECT. II. 115 

what is included in the Middle term — that is, one kind 
of habits — and found to agree with it ; and the Minor 
term is compared with the other part. 

II. Of the Moods of Syllogisms. 

471. The Mood of a Syllogism is that which indi- 
cates the nature and order of the Proposi- The Mood of 
tions which constitute it. As any one of the syiiogisms. 
Four Judgments may be the Major Premise, Minor 
Premise, or Conclusion, it is seen by permutation and 
combination that there may be sixty-four Moods. 

472. But by no means all of the sixty-four Moods 
are valid in any Figure, and of those that are ^^^ ^ii Moods 
valid, not all are valid in all four of the ^^*'^- 
Figures. Hence we must effect what is called an 
ccbscissio infiniti — that is, a continued cutting oif of 
the several classes of invalid Moods, until we get them 
reduced so as to include none that are not valid. 

473. From the Diagrams and remarks upon them 
just given, it will appear with regard to the Quality 
of the Conclusion, that 

(1.) If both Premises are Affirmative, and the Middle 
term be once distributed, the spheres of the Quality of the 
Extremes must be in part at least coinci- Conclusion, 
dent ; that is, the Conclusion must be Affirmative also. 

(2.) If either Premise be negative, and the other 
affirmative, and the Middle distributed, then the Ex- 
tremes must represent contrary spheres ; that is, the 
Conclusion will be negative. 

474. In regard to the Quantity of the Conclusion, 
the Rule is that "No term may be distri- Quantity of the 
buted in the Conclusion, which was not dis- conclusion. 
tributed in the Premises." Any violation of this Rule 
is a Fallacy in Form, and is called Illicit Process, It 
may be of two kinds. Illicit Process of the illicit process. 
Minor ^ and Illicit Process of the Major. 

We have two cases in which the Minor term may 
be illicit in the Conclusion. 



116 LOGIC. PAKT I. [chap 

(1.) When the Minor term is Subject : No more of 
Of the Minor tlie Minor term can be either included in 
first case. ^j. excludcd from the Major by means of the 
Middle than is included in the Middle itself. 

(2.) When the Minor term is Predicate only that 
Second case, part of it which is coincident with the Mid- 
dle, can be included in or excluded from the Major by 
means of the Middle ; or if the Minor term is excluded 
from the Middle, then no more of it is excluded from 
the Major by means of the Middle than is excluded 
from the Middle itself — this will be seen from the 
preceding Diagrams. 

475. As Affirmatives do not distribute the Predi- 
No Illicit of the cate, there can be no Illicit Process of the 
co^nduTiolis. ""^ Major, except when there is a Negative 
Conclusion. 
M^ajof ""^ ^^^ 4:76. We may have two cases : 

(1.) When the Major term is Predicate. If the 
Premise is Negative the Major term is of course dis- 
Firstcase. tributcd. But if the Premise is Affirmative, 
then the Major term as Predicate must be taken as a 
whole ; and as such it can comprehend nothing which 
is not in the Middle term. But if it be not taken as a 
whole, the Minor term may be in that part of the 
Major which is not occupied by the Middle term. 

Thus let us have a large circle P, includ- 
ing M and something more. Thus S may 
be in the part of P, not occupied by M, 
without being in M, thus we may have : 
M is P, 
S is not M, and S may or may not be P. 

(2.) But in the second case if the Major term is 
Second case, subjcct iu the Prcmisc, it must be wholly 
included in M, or S may be in that part of it which 
is not included in M. 

Thus let us have a large circle M, and 
another P only part included in it. Then 
S may be in the part of M which is not in- 
cluded in P. 





in.] OF SYLLOGISMS. SECT. II. 117 

Then we have Some P is not M, 

S is M, 
and S may or may not be P ; 
Or suppose some in P only is in M and the rest not, 
and then we may have — Some P is M, 

S is not M, 
in this case too, S may be or may not be P. 

477. From what has been said, it will appear, 

1. That if both Premises are negative. Five canons of 
we can have no Conclusion. validity. 

2. If one Premise is negative the Conclusion must 
be negative. 

3. If both Premises are affirmative the Conclusion 
must be affirmative. 

4. The Middle Term must be distributed in one of 
the Premises ; and 

5. No Term may be distributed in the Conclusion, 
which was not distributed in the Premises."^ 

478. By the First of these Pules the sixteen Moods 
with negative Premises are excluded from The First ex- 
being valid in any Figure. By the Second, ^^^||. '^^^^^" 
the sixteen with one negative Premise and second, six- 
affirmative Conclusions; and by the Third, teen more, 
the eight with affirmative Premises and a m™"^^' ^'^^^ 
negative Conclusion. 

479. By the Fourth and Fifth combined, all those 
Moods in which both Premises are particu- Fpurth & Fifth, 
lar, are excluded ; since if both are particular ^^''• 

(and one must be affirmative), there can be but one 
term distributed in the Premises — and if both Pre- 
mises are affirmative, there will be none. In this 
case there will be undistributed Middle. But if one 
Premise is negative the Conclusion must be so too, 

* The folloAving hexameters have been found to assist the memory in 
retaining these fundamental requirements of simple Categorical Syllo- 
gisms : 

Distribuas Medium : nee quartus terminus adsit 
Utraque nee praemissa negans, nee particularis : 
Sectetur partem Conclusio deteriorem : 
Et non distribuat, nisi cum Praemissa, negetve. 



118 LOGIC. PART I. [chap. 

and then we shall have either Illicit Process of the 
Major or Undistributed Middle. 

480. By the operation of the same rules. Fourth and 
Six more. Fifth, it will bc fouud that if one Premise 
be particular there can be no universal Conclusion. 
(1st) Suppose the conclusion to be A ; in order to that, 
the Premises must be both affirmative — and with one 
of them. Particular Affirmative — there will be but one 
term distributed in the Premises, if that be the Minor, 
we shall have undistributed Middle, and if the Middle 
we shall have illicit of the Minor. (3d) Suppose the 
conclusion to be E, one Premise must be negative, and 
all three terms distributed in the Premises. But there 
are no Premises that fulfil this condition, except A 
and E, and O and E. But O and E are both negative, 
and can have no conclusion ; A and E are universal, 
and therefore do not come under this rule. 

481. By the same reasoning it will be found that 
lEo. lEO will involve an Illicit Process of the 
Major in all the Figures.^ 

482. The eleven valid Moods are — AAA, A AI, 
Eleven vaud. AEE, AEO, All, AGO, EAE, EAO, EIO, 
lAI and OAO. 

483. Not all of these, however, are valid in each 
of the Four Figures which we have just described. 

III. The Application of Moods to the Figures. 

484. In the First Figures (1) if the Major Premise 
Application of bc particular we can have no Conclusion — 

FiS' Figure, for {o) if thc Miuor be Affirmative we should 

* The Moods excluded by these Rules are : 

By the First— EEA, EEE, EEI, EEO, EOA, EOE, EOI, EOO, OEA, 
OEE, OKI, OEO, OOA, OOE, 001, and 000— (16). 

By the Second— EAA, EAI, AEA, AEI, EIA, EII, lEA, lEI, OAA, 
OAI, AOA, AOI, OIA, Oil, lOA, lOI— (16). 

By the Third— AAE, AAO, AIE, AIO, lAE, lAO, HE, 100— (8). 
By the Fourth and Fifth— (1) OIE, 010, lOE, HA, III, HO— (6). 

(2) AOE, OAE, IA.\, lEE, AIA, EIE— (6). 
*' " (3) lEO— (1). 

In all 16 + 16 + 8 + 6 + 6 4- 1 = 58. 



in.] OF SYLLOGISMS. SECT. II. 1 19 

have an undistributed Middle ; and (J) if Negative, the 
Conclusion must be Negative also, and that would in- 
volve an Illicit Process of the Major. 

(2.) If the Minor be Negative there can be no Con- 
clusion ; for the Major Premise would have to be 
Affirmative, and that would involve an Illicit Process 
of the Major. 

Hence in the First Figure the Major Premise must 
be A or E, and the Minor A or I, and we six vaiid-four 
may have AAA, AAI, EAE, EAO, All, ^^^^^• 
EIO. 

But as AAI and EAO have particular conclusions, 
when we might have from the same Premises an uni- 
versal one, they are useless and so dismissed from fur- 
ther consideration. 

485. These Four Syllogisms are called Barbara^ 
Celarent^ Darii^ and Ferio!^ Names. 

486. In the Second Figure. If both Premises are 
Affirmative we can have no Conclusion ; second Figure, 
since the Middle term, being Predicate in both, would 
be undistributed. 



* As examples we may have the following : 

Barbara, " Those who derive benefit from every exertion of their indus- 
try, are more likely to be industrious than laborers employed by the day. 
Journeymen who work by the piece derive benefit from every exertion of 
their industry ; therefore journeymen who work by the piece are more 
likely to be industrious than laborers employed by the day." 

Celarent. " No real hardship upon individuals should be authorized by 
legislative enactment. The impress of sailors is a real hardship upon indi- 
viduals, therefore the impress of sailors should not be authorized by legis- 
lative enactment." 

Darii. " Every thing which obstructs the free course of justice deserves 
the reprobation of the virtuous. There are modes of enforcing the strict 
letter of the law which obstruct the free course of justice ; therefore there 
are some modes of enforcing the strict letter of the law which deserve the 
reprobation of the virtuous." 

Ferio. " Those who endure dangers and face death merely for the sake 
of acquiring glory to themselves, without being influenced by any desire to 
benefit their country, are not possessed of true fortitude. But it cannot be 
denied that some of the heroes of antiquity endured dangers and faced 
death, merely for the sake of acquiring glory to themselves, without being 
influenced by any desire to benefit their country. Consequently several of 
the heroes of antiquity were not possessed of true fortitude." 



120 LOGIC. PART I. [chap. 

And if the Major Premise be Particular there can 
be no Conclusion, since that would involve an Illicit 
Process of the Major. 

Hence we have in the Second Figure — AEE, AEO, 

sLx valid-four EAE, EAO, EIO, and AGO. But AEO 

and EAO have particular Conclusions when 

we might have universal, and hence they are dismissed 

as useless. 

487. It will be observed, that all the Conclusions 
c^ndSs^'''^ in this Figure are Negative. 

488. The four valid and useful Syllogisms in the 
Examples. Figurc are called Oesare^ Camestres^ Festino^ 
and BaroJco,^ 

489. In the Third Figure there can be no Universal 
Third Figure. Conclusiou — for iu ordcr to such a Conclu- 
sion both Premises must be Universal ; but if both are 

No Universal Affirmative, the Minor term will be undis- 
conciusions. tributed, and hence a Universal Affirmative 
would be Illicit of the Minor ; and if the Minor be 
Negative the Major Premise must be Affirmative, and 
that would give an Illicit Process of the Major in a 
Negative Conclusion. And for the same reason there 
can be no conclusion if the Minor Premise be a Nega- 
tive. 

490. Hence in the Third Figure we can have only 
Six valid names. AAI, All, EAO, EIO, lAI aud OAO. 

* For examples take the following : 

Cesar e. " No conscientious person wilfully violates a solemn engagement. 
Every careless clerg3Tnan wilfully violates a solemn engagement ; therefore 
no careless clergyman is a conscientious person." 

Camestres. " All those who are qualified for sea-service must possess 
some knowledge of the arts of navigation. Mere inland watermen do not 
possess any knowledge of the arts of navigation ; therefore mere inland 
watermen are not qualified for sea-service." 

Festino. " No man of sound sense can despise the study of the classics. 
Some modern pretenders to literature do, however, despise the study of the 
classics ; therefore some of the modern pretenders to literature are not men 
of sound sense." 

Baroho. " All the fixed stars emit light from themselves. Yet there are 
some of the heavenly bodies which do not emit light from themselves ; 
therefore some of the heavenly bodies are not fixed stars." 



i 



Til.] OF SYLLOGISMS. SECT. II. 121 

The six Syllogisms of the Third Figure are Darapti^ 
Disarais^ Datisi^ Felajpton^ Bokardo^ and F'eriso.^ 

491. In the Fourth Figure, with A for Major, we 
must provide for the distribution of the Mid- Fourth Figure, 
die term in the Minor Premise by making that Premise 
Universal. If then the Minor Premise be A, we may 
have I for Conclusion (A would be illicit of the Major). 
If the Minor Premise be E, we may have E and O 
for Conclusions. But O is useless. Hence AAI and 
AEE. 

With E for Major Premise the Minor must be 
affirmative. If A, we have O for Conclusion (E would 
be illicit of the Minor). If it be I, we have O also for 
Conclusion. Hence EAO and EIO. 

With I for Major we must have A for Minor to dis- 
tribute the Middle, and hence I is the only Conclusion. 
Hence lAI. 

With O for Major we must have a negative Con- 

* Examples : 

Darapti. " To be ashamed of one's birth, profession, or rank in life, has 
been represented as the fault of modesty — whereas in reality it is a symp- 
tom of pride ; so that even that which is a symptom of pride has been repre- 
sented as the result of modesty." 

Disamis. " Some practices which the divine law allows are under parti- 
cular circumstances inexpedient. All practices which the divine law allows 
however are in themselves consistent with holiness ; therefore some things 
which are in themselves consistent with holiness are under particular cir- 
cumstances inexpedient." 

Datisi. " Every kind of pride is wholly inconsistent with the spirit of 
religion. Yet there are several kinds of pride which are highly commended 
by the world, therefore there are feelings highly commended by the world 
which are wholly inconsistent with the spirit of true religion." 

Felapton. " No conspiracies against the liberty of the country lay any 
just obligation on the conscience. All such conspiracies, however, have the 
nature of contracts ; hence some contracts do not lay any just obligation 
upon the conscience." 

Bohardo. " Some compositions of an imitative nature, calculated by sub- 
limity of idea and beauty of diction to expand and delight the mind and to 
excite every noble passion, are not written in verse. All such compositions, 
however, are called poems ; therefore some works justly called poems, are 
not written in verse." 

Feriso. " No prejudices are compatible with a state of perfection — but 
some prejudices are innocent ; therefore some innocent things are not com- 
patible with a state of perfection." 

6 



122 LOGIC. — ^PAKT I. [chap. 

elusion, which would involve an Illicit Process of the 
Major. 

Hence in the Fourth Figure we have AAI, AEE, 

Five valid Forms. EAO, EIO, and lAI. 

492. The five valid and useful Syllogisms in the 
Fourth Figure are, Bi'amantvp^ Camenes^ Dimaris^ 
Fesa^o^ and Fresison.^ 

493. Of the Eleven valid Moods, we have AAA 
Recapitulation. Valid oulj iji the First Figure ; AAI in the 
First, Third, and Fourth, but useless in the First ; 
AEE valid in the Second and Fourth ; AEO in the 
Second and Fourth, but useless in both ; All valid in 
the First and Third; AOO in the Second; EAE in 
the First and Second ; EAO in all, but useless in the 
First and Second ; EIO valid in all Figures ; lAI in 
the Third and Fourth ; OAO in the Third. 

494. In the whole, then, we have Nineteen valid 
Nineteen valid and uscful elementary Forms in Pure Cate- 
sy ogi=,ms. gorical Syllogisms ;^their names have al- 
ready been given. But for the convenience of remem- 
bering, especially for those who understand Latin 
Prosody, they have been arranged into the following 
lines : . 

BArbArA, CElArEnt, DArll, FErlOque, ^W(?r/5 / 
CEsArE, CAmEstrEs, FEstInO, BArOkO, secun- 

Tertia, DArAptI, DIsAmIs, DAtlsI, FElAptON ; 
BOkArdO, FErlsOn habet : Quarta inswper addit 
BrAmAntIp, CAmEnEs, DImArls, FEsApO, FrE- 
slsOn. 

* Examples : 

Bramantip. " All diamonds consist of carbon— but all carbon is com- 
bustible ; tberefore some combustible substances are diamonds." 

Camenes, " All the planets are opaque bodies. No opaque bodies are 
capable of transmitting light in any other way than by reflection ; therefore 
bodies capable of transmitting light in other ways than by reflection are not 
planets." 

Dimaris. " Some of the inhabitants of the sea have antennae and homy 
Jointed legs — but all animals of this description are insects ; therefore some 
^lsects are inhabitants of the sea." 



in.] OF SYLLOGISMS. SECT. III. 123 

The vowels printed in capitals will be recognized 
as indicating the Mood of the Syllogism, and the con- 
sonants besides making out the words serve another 
purpose, to be explained by and by. 



SECTION m. 

Of Indirect Conclusions, 

495. There has sometimes been reckoned a class of 
Indirect Moods, but this is unnecessary ; indirect Moods, 
since all that are reckoned as Indirect Moods are merely 
some one of the Direct Moods with the Premises trans- 
posed. 

Thus for example. All B is A, 

ITo is B, 
.*. Some A is not C. 
This is simply Fesapo with the Premises transposed, 
and the Indirect Conclusion. 

496. An Indirect Conclusion is one in which the 
order of the terms of the Direct Conclusion indirect con- 
is inverted, so as that the Subject becomes viTseSf theX 
Predicate, and vice versa / and an Indirect '■^^*' 
Conclusion is valid when (1) it does not change the 
quality of the Direct Conclusion ; nor (2) distribute 
any term in the Indirect Conclusion which was not 
distributed in the Premises. 

497. It is worth while to notice, however, that in 
most cases we may have an Indirect Conclusion as well 
as the Direct.^ Thus — Barbara : 

Fesapo. " No vice is to be admitted as a species of relaxation suited to a 
Cliristian. Every species of relaxation suited to a Christian consists of a 
cessation from ordinary occupations. 'V\'Tierefore there are cessations from 
ordinary occupations which are not vice." 

Fresison. " No fallacious argument is a legitimate mode of persuasion. 
And some legitimate modes of persuasion fail of securing acquiescence ; 
therefore some arguments which fail of securing acquiescence are not fal- 
lacious." 

* In fact it will he seen that all the Conclusions in the Fourth Figure 
are but the Indirect Conclusion from the same Premises, regarded (by con- 
adering the Major term as Minor, and vice versa) as in the First Figure." 



124 LOGIC. — PART I. [chap. 

Indirect Con- ^^^ ^ ^^ ^y 
elusions in all A 1 1 7 i o ^ 
Syllogisms. -^^^ Zj lb ± ^ 

.'. All Z is X — or indirectly, Some X is Z. 
Bramantip gives a more important Indirect Con- 
clusion still : 

All X is Y, 
All Y is Z, 
.-. Some Z is X — or indirectly, All X is Z. 
In the Direct Conclusion the Major term appears 
as undistributed in the Conclusion, whereas it was dis- 
tributed in the Major Premise. 

498. Besides the above-named nineteen Syllogisms, 
any other of the valid Moods may have an incidental 

Incidental va- Validity, if its tcrms are so distributed either 
lidity. i^y signs or the nature of the terms, or of the 

matter of the judgment as to secure lis against Undis- 
tributed Middle and Illicit Process. 

499. Again, if we have two affirmative Premises in 
Analogy prov- thc Sccoud Figurc, both extremes are in the 

Figiie. ^'^^ same category — the Middle term ; and then 
they must each of them have the Essentia of the concep- 
tion which the term denotes. They have therefore so 
much matter in common — that is, so many points of 
identity, and consequently there is an analogy between 
the Extremes. 

SECTION IV. 
Of the Conversion of Syllogisms, 

500. It has been thought that all Mediate Inference 
could be reduced to the celebrated Dictum of Aris- 

Aristotie's totlc. Called the Dictum^ de Omni et Nullo ; 
Dictuno. ^i^^i- jg^ u Whatever may be predicated of a 

* Aristotle appears to have thouglit that all Mediate Inference could he 
reduced to this one Canon. And so by Conversion it can. But later writ- 
ers have given us dicta for each of the other Figures (Lambert, Neues 
Organon, Part I. ch. 4, § 232). 

That for the Second Figure is called the Dictum de Diverso : " If a cer- 
tain attribute can be predicated (affirmatively or negatively) of ever^- 



ni.] OF SYLLOGISMS. SECT. IV. 125 



• 



class [the Middle term], may be predicated as Major 
term of whatever is comprehended in that class, as a 
Minor term ; and conversely whatever may be denied 
of that class may be denied of whatever is compre- 
hended under it." 

501. This is substantially the same as the first 
Axiom of Mediate Inference which we have given 
(464) ; and to prove that all cases of Mediate Inference 
can be reduced to it, various expedients have been de- 
vised for reducing the Syllogisms of the Second, Third, 
and Fourth Figures to Syllogisms in the same matter 
in the First Figure. 

502. If this were the only object to be gained in the 
Reduction of Syllogisms, as it is called, it objects of Re- 
would hardly be worth the time and pains ^^'^^^^ion. 
which it costs, since the other axioms given above are as 
primary and as satisfactory as the Dictum of Aristotle 
itself. But there is a further practical importance in 
the Reduction of Syllogisms which makes it worth 
our while to examine the laws and processes by 
which it can be done. Such is the nature and imper- 
fections of language that we cannot always express our 
judgments exactly as we would, *and many an expres- 
sion which suits all the requirements of Logic, fail to 
meet the demands of Rhetoric. 

503. In order to effect this Reduction or Conver- 
sion, we need to resort to Conversion, Per- Means of con- 



version. 



mutation, and Transposition of Premises, one 
or the other of them, and sometimes more. 

member of a class — any subject of which it cannot be so predicated does not 
belong to that class." 

The Third Figure (1) Dictum de Exemplo : " If a certain attribute can 
be affirmed of any portion of the members of a class, it is not incompatible 
with the distinctive attributes of that class ; " — and (2) the Dictum de Excepto : ' 
" If a certain attribute can be denied of any portion of the members of a 
class, it is not inseparable from the distinctive attributes of that class." He 
also gives what he calls a Dictum for the Fourth Figure, which he calls 
the Dictum de Reciproco. But it is hardly worth quoting. The Fourth Figure 
is at best but an inverse of the First, and depends upon the same Principle 
inverted. For the above quotations I am indebted to the Oxford edition of 
Aldrich, 1849, pp. 72 and 80. 



126 LOGIC. ^PAET I. [chap. 



Conversion and Permutation of Propositions have 
already been sufficiently explained. 

504. Transposition consists merely in changing the 
Transposition rclativc posltiou of the Premises : thus, for 

of Premises. ^ ' ' 

^ ^^ ^' I we shall have i S is M, 
.-. S is P, .-. S is P. 

This it will be observed is not changing the Syllo- 
gism from one Figure into another. It is merely writ- 
ing the Minor Premise first instead of the Major. Sir 
William Hamilton says that this was generally done 
for several centuries after Aristotle. And we shall see 
by and by that in practice, where we are guided by 
instinct and common sense, with no regard to Logical 
Formulae, we usually state the Major Premise first 
in the Deductive Methods, and the Minor first in the 
Inductive Methods. 

505. But as the transposition changes neither the 
quantity nor the quality of the Premises, nor yet the 
relative position of any of the terms in regard to the 
laws of the distribution of terms by Position, it can 
have no effect upon, the concluding force of the Pre- 
mises. 

506. In these cases we obtain the result in three 
Different forms different forms — we may get (1) the same 
sion. "^ **"^ '^' Conclusion in the Converse as in the Exposita ; 
or we may get (2) one from which that is derived as 
an Immediate Inference ; and we may get (3) a Con- 
clusion contradictory to that of the Exposita, but false ; 
from which of course the truth of that in the Exposita 
is inferred immediately. 

507. It is with reference to this process of Conver- 
sion of Syllogisms, that the Consonants used in the 
Signification of namcs that have been given to them are 
t^ie^^Names o"f sclccted ; thc Yowels are used to indicate 
Syllogisms, ^]^^ Mood. But tlic Consouauts indicate the 
processes and means of converting them into Syllo- 
gisms in the First Figure. 



m.] OF SYLLOGISMS. SECT. IV. 127 

All beginning with B, can be proved in Barbara. 
" C, " " " " Celarent. 

a u u j)^ u u u u j)^j.- 

a u u F, " " " " Ferio. 

The steps to be taken are indicated as follows : 

"m" denotes that the Premises are to "m» transpose! 

-1 , -I Premises. 

be transposed. 

" s " denotes that in order to reduce a Syllogism to 
the First Figure, the Proposition signified u^„ converts 
by the vowel before the s is to be converted '^"^p^^- 
simply. 

Thus the Minor Premise in Camestres — No Y is Z, 
is to be converted into No Z is Y. 

"p " denotes that the Proposition indicated by the 
vowel before it, is to be converted by limita- "^^^ converts 
tion, or per accidens, ^eracadens. 

'' y^ " occurs in Baroko and Bokardo only. These 
are reduced to Barbara by what is called reductio ad 
impossihile. The reduction is effected by "&"gi.vesa 
substituting the contradictory of the Conclu- cZcfusfon.'^ 
sion for the Premise, indicated by the vowel imme- 
diately before the " yfc," and proceeding as before.*^ In 
this way we get a Conclusion contradictory to the Pre- 
mise for which we have substituted the contradictory of 
the old Conclusion. If now the new Conclusion is false, 
or absurd, or impossible, the old one must have been 
true. We are in fact proving that the Conclusion is 
O, by the indirect method of proving that it cannot 
be A. 

508. In the course of these reductions, it will be 
observed that the terms undergo several rela- change of 
tive changes, so that Major becomes Minor, '^^'■'^^• 
&c., and vice versa. In that case the name of the Syl- 
logism ends in "5" or "^," — as " Camenes," " Bra- 
mantip." The Middle term also in Baroko and Bokardo 
becomes one of the Extremes. 

* These rules have been expressed in the following lines : 
S vnlt simpliciter verti ; P vero per acci- 
M vult transponi ; K per impossibile duci. 



128 LOGIC. PART I. [chap. 

509. When in the course of the Conversion or Re- 
duction of Syllogisms we get a Conclusion in the same 

ostensive qualitj as that in the Exposita Syllogism, 
Reduction. ^j^^ proccss has been called Ostensive Reduc- 
tion, But if the Conclusion be in the opposite quality, 

Reductio ad ^hc Ecduction is called Seductio ad Invpos- 
Absurdum. sibiU^ OT Eeductio ad Absurdum. 

510. As examples in Ostensive Reduction, I will 
Examples. give ouly a few, as follows : 

Cesare to Celarent, 

No X is Y, s. No Y is X, 

Cesare. All Z is Y, the Miuor stands, All Z is Y, 
.-. No Z is X, .-. No Z is X. 

Darapti to Darii. 

All Y is X, the Major stands, All Y is X, 
Darapti. All Y is Z, p. Somc Z is Y, 

.-. Some Z is X, .*. Some Z is X. 

Bramantip to Barbara. 

All X is Y, ) ( All Y is Z, 

Braman. All Y is Z, \ '^' | All X is Y, 

.'. Some Z is X, .-. Some X is Z, p Some Z is X. 

Felapton to Ferio. 

No Y is X, No Y is X, 

Felapton. All Y is Z, p. Somc Z is Y, 

.-. Some Z is not X, .-. Some Z is not X. 

Fresison to Ferio. 

NoXisY, s. NoYisX, 

Fusison. Some Y is Z, s. Some Z is Y, 

.-. Some Z is not X, .'. Some Z is not X. 

511. Reductio ad Impossihile is effected by means 
of Contra-position and Excluded Middle. 

Baroko. Thus if wc liavc in Baroko : 

Every star is fixed. 

Some luminous bodies are not fixed. 
.-. Some luminous bodies are not stars (such for in- 
stance as planets, meteors, &c.) 



i 



m.] OF SYLLOGISMS. SECT. IV. 129 

Let us substitute for this Minor Premise the contra- 
dictory of the Conclusion and we shall have : 
Every star is fixed. 
All luminous bodies are stars. 
.'. All luminous bodies are fixed. 
But this Conclusion is false, consequently the Mi- 
nor Premise of the first Syllogism, Baroko, its contra- 
dictory, is true. And if that Premise is true (the 
Major Premise also), the Conclusion is irrefragable. 
In the same way we may test Bokardo. 

512. Or again, we may reduce Bokardo by contra- 
position of the Major to Ferio ; thus, Baroko to 

All X is Y, ^^"«- 

Some Z is not Y, 
.-. Some Z is not X. 
All X is Y, we may state by contra-position and 
conversion in E. — No non-Y is X, then we have as 
before, Some Z is not Y or non-Y, 

.-. Some Z is not X, 
which gives us the same conclusion in Ferio as we had 
in Baroko. 

513. Again, we may reduce Bokardo to Darii, by 
permuting, and converting, and transposi- Bokardo to 
tion, as follows : ^^^'• 

Some slaves are not discontented. But 
All slaves are wronged. 
.'. Some who are wronged are not discontented. 

We may have : 

All slaves are wronged. 
Some not-discontented persons are slaves. 
.-. Some not-discontented are wronged. 

514. This process of Reductio ad Impossibile may 
be applied to all Syllogisms, as well as to process appu- 
Baroko and Bokardo, on the ground that if ^^bietoaii. 
we substitute for any given Premise the contradictory 
of the Conclusion, we shall obtain for a new Conclusion 
the contradictory of the Premise; or its contrary, in- 
which, of course, the contradictory is included. 

6^ 



130 LOGIC. — PART I. [chap. 

Thus Barbara to Bokardo, 

All Y is X, ) by contra-posi- ( Some Z is not X, 
iokSdo'" All Z is Y, \ tion of the Con- \ All Z is Y, 

.-. All Z is X, ) elusion becomes ( .*. Some Y is 

not X. 
Thus from Oelarent we may have Disamis in the 
Third Figure, and Festino of the Second. 

ceiarent No Y is X, Somc Z is X, or, No Y is X, 
Ind'teTt" All Z is Y, All Z is Y, Some Z is X, 

°^- .-. No Z is X, .-. Some Y is X, .-. Some Z is not Y. 

515. It is often very important in general discus- 
sions to disembarrass ourselves of the details of Mood 
and Figure, and speak of Terms and Premises in the 
most general way ; even where the Differentia of the 
Figures would require, if they were recognized at all, 
a very important modification of our statement. 

516. For this purpose we always consider an argu- 
omission of mcut, uulcss othcrwisc expressly stated, as 

FillJre^"*^^^ *^ made in the First Figure, and when we speak 
of the Major Premise we mean that which either is 
the Major in the First Figure, or that which would 
become the Major if the Syllogism were converted into 
that Figure. And for the same purpose we consider 
all Negative Propositions as Affirmative with Nega- 
tive Predicates, as we have a right to do. And hence 
we may always speak of that term which either is or 
would become on conversion of the Syllogism into the 
First Figure the Predicate of the Conclusion, as the 
Major term. If the Conclusion be affirmative that is the 
Major term, and if not we substitute for the Predicate 
of the Negative Conclusion its connoted negative or 
privative, which of course becomes a Major to the 
others. 

517. This may, perhaps, be thought to indicate a 
Indicates no looscncss aud Uncertainty with regard to the 

bSSt T^?Js. ^" whole nomenclature of Mood and Figure, 

which does not exist. But we have to take an argu- 

'ment for the most part as we find it. And as it thus 

stands, it is no matter of choice or uncertainty which 



in.] OF SYLLOGISMS. SECT. V. 131 

are the Major and Minor terms hj position. But to 
avoid the perplexity and the prolixity of continued 
repetition or detail, we may avail ourselves of the fact 
that all the Syllogisms may be reduced to the First 
Figure ; that is, the fact that with the same matter as 
that given in the Premises, we may prove the same 
Conclusion in the First Figure, and thus adopt the 
simplicity and brevity of discussion which there would 
be if there were only the one Figure. 



SECTION V. 
Of Complex Syllogisms, 

518. We have thus far in the investigation of the 
laws and formula of Syllogisms spoken only of the 
Simple Categoric Syllogisms. Although this is the 
simplest and primary formula, we but sel- 

T -^ i 'xi j1 • .• T ^ Seldom meet 

d.om meet with tnem m practice. In nearly Pure and sim. 

V ii > • "^ pie Formulas. 

every case one or more ot the terms is com- 
plex. Hence a Syllogism in w^hich one or more terms 
has a modal, is called a Complex Syllogism. 

519. Strictly speaking the simple term can be 
nothing more than a single word ;"^ which is simple Terms, 
either a noun, an adjective, or a verb in the Infinitive 
Mood. In adjectives I include participles used ad- 
jectively. 

520. But it often happens that several words are 
used as the definition of a term instead of Definition for 
the term itself. Thus we have the term ^ '^^""• 
Negro — but instead of it we may use its definition in 
any case — as " men with darh skins and woolly hairy 
&c. Now suppose that we had not the word " Negro " 
at all. In that case we should be obliged to use its 

* This must depend, however, somewhat -upon the genius of a language. 
Perhaps the only exception, the only one that I have noticed in the English, 
is in those words which answer to the Aristotelian category " wkere^ We 
say a man is "in the house," — "on the ground," &c., &c. We have not 
in this respect any thing corresponding to the Greek termination Q1 as in 
aypoOij oiKoOi, &c. 



132 LOGIC. — PART I. [chap. 

definition whenever we wish to use the conception as a 
term at all. 

521. This is precisely the case with regard to a 
Necessity for it. large part, by far the largest part of the 
conceptions which enter into our reasonings. There is 
no precise term for them ; and therefore we are obliged 
to use, instead of the term, what is really its definition. 
The Definition gives first the Genus and then the Dif- 
ferentia one after another. Thus for " Negro " we have 
[genus] men, — [1st diflferentia] with dark skins, — and 
[2d differentia] woolly hair. Suppose we wish to speak 
of those Christians who adhere strictly to their faith 
and live pious and devoted lives, as a class distin- 
tinguished from the rest, we have no one word by 
which to denote the class. Consequently when we 
want to express the conception, we are obliged to use 
the definition for want of a word to denote it. 

522. In all such cases we may, if we please, regard 
Definition, a thc Definition as the Term and its Logical 

ModSis^^ ^^ Modals, or as a simple term for all the ordi- 
nary purposes of deduction. 

523. All Modals which have any logical force at 
Modals limit all, as has been shown, either limit the com- 

the comprehen- \ . x» ^.i i • ^ • i? i. 

siveness of the prehensivencss oi the subject m reierence to 
^'^' quantity, or point out some condition, or 

time necessary to limit the scope of the judgment in 
order that it may be true. Hence the Modal will often 
make the whole of the difference between a Propo- 
sition that is true and one that is false. 

But as Rhetoric often requires some variety in ex- 
pression, the phraseology of Modals must often be 
changed, and in these changes Fallacies often occur. 

524. The Modal of a subject limits the scope of the 
Modals of the judgment, by limiting the sphere of the 

tll^eicopeofthe subjcct itsclf. Now from the fundamental 
Judgment. ^xiom, that the narrower the sphere the 
greater the amount of the matter of any conception, it 
follows thab more may be predicated of a subject which 
is limited by a modal than can be predicated of the 



m.] OF SYLLOGISMS. SECT. V. 133 

same term without the Modal. Hence the dropping of 
the Modal would in some cases render the Proposition 
untrue. 

525. Suppose now that the Middle term is first used 
with a Modal, and is used in the next Pre- ^j^die Term 
mise without one, we have in fact a different "^'^^ ^ ^®^^^- 
term ; and it will afiect the formula differently accord- 
ing to its position. 

Let us then refer to the First Figure in which the 
Middle term is Subject of the Major Premise ^n t^e First 
and Predicate of the Minor. If we drop the ^'^'^^®- 
Modal in the Minor term we enlarge the sphere denoted 
by it, and by consequence it may become so large that 
the Major term could not be predicated of it. Thus, 

All true Christians enjoy the favor of God. 

Hypocrites are Christians. 
,-. Hypocrites — 
But here it becomes obvious that the matter of the 
Predicate in the Major Premise could not be predicated 
of so comprehensive a sphere as " Christians ; " that is, 
" all Christians," — nor the Differentia of true Christians 
of the subject of the Minor Premise. 

526. Now let us take an example of the opposite 
course : 

All Christians believe in Christ. 
The Waldenses were true Christians. 
.-. The Waldenses, &c. 

Here the conclusion is good. We include the Minor 
term by means of the Modal in a narrower and com- 
prehended sphere than that which, as Middle term, 
we had included in the Major term in the Major Pre- 
mise. 

527. We have already seen that the Middle term 
must be once distributed in the Premises of a Syllo- 
gism, and in fact it is distributed in both Premises in 
two of them, Darapti and Felapton. But wherever it 
occurs as an undistributed term, it stands of course for 
a narrower though an undetermined sphere than if it 



134 LOGIC. PART I. [chap. 

were distributed. We have the following Rules for 
Three Rules, the dropping or assuHiption of Modals in the 
same Syllogism. 

(1.) In all cases where the Middle term is undis- 
First Rule. tributcd, as always in the Minor Premise in 
the First Figure for instance, we may always make the 
indeterminate undistributed term a determinate dis- 
tributed term, with a narrower sphere than the abso- 
lute or simple term, by joining to it its appropriate 
Modal. And when the Middle is twice distributed as 
in Darapti, and Felapton, and Fesapo, we may limit it 
in either Premise at discretion, but not in both unless 
it be with the same Modal. 

(2.) And conversely a Modal that w^as introduced 
Second Rule, and uscd with the Middle term when used 
distributively, may not be omitted where it occurs in 
the other Premises as an undistributed term. This 
remark, for a reason similar to the one given in case 
of the last rule, does not apply to Darapti, Felapton, 
and Fesapo, in which the Middle term is distributed 
in both Premises. 

(3.) And finally, if the undistributed Middle occurs 
Third Rule. in thc Major Premise, as in the Fourth Fi- 
gure with a Modal, that Modal may be dropped when 
the Middle term comes to be used as a distributed 
term in the Minor Premise. 

(4.) If in the Major Premise a Modal is used, 
extending the comprehensiveness of the judgment to 
Expansive ^^^ possiblc cascs, thcu either in the Minor 
Modals. Premise or in the Conclusion we may have 

one pointing to any special case or class of cases, 
included within the comprehensiveness to which the 
Modal of the Major Premise extended it. Thus : 

" No man is justified on any pretence in taking the 
life of one with whom he is living on terms of con- 
fidence.'' 

" But Brutus was living on terms of confidence with 
Csesar." 

" Therefore Brutus was not justifiable in taking 



m.] OF SYLLOaiSMS. SECT. V. 135 

Caesar's life on the pretence which he pleaded — of a 
higher obligation to his country P 

(5.) In regard to the Minor term, if it was used 
without a Modal in the Minor Premise it Modaisofthe 
was used in its most comprehensive sense ; ^"^^ '^^^°^^- 
hence if we annex a Modal in the Conclusion we sim- 
ply narrow the sphere of the subject, which as we have 
before seen does not render the Proposition untrue. 
But if the Minor term had a Modal in the Minor Pre- 
mise, it may not be omitted in the Conclusion, since 
that would enlarge its sphere and possibly include 
thereby individuals of whom the predicate may not be 
affirmed. 

(6.) And in regard to the Major term the converse 
holds. If there was a Modal in the Major Modaisofthe 
Premise it may be omitted in the Conclu- ^^J**^ '^^™^' 
sion, as by so doing we enlarge its sphere and con- 
sequently include less matter. If therefore it was pre- 
dicable of the subject before the enlarge- cenereiRuie 
ment of its sphere, then a fortiori it is after- Ssum^ng"! mS^ 
wards. But if the Major term was in the *^^- 
Premise without the Middle, no Modal can be intro- 
duced into the Conclusion, except that which was 
spoken of above as changing the indeterminate undis- 
tributed into a determined distributed, denoting the 
individuals included in the scope of the subject as a 
species. 

528. We may then lay down the general proposi- 
tion that a Modal may at any time, and in General pro- 
any position be attached to an undistributed ^ssimption of I 
term, provided the Modal expresses the dif- ^°'^^^- 
ferentia or peculiar property of that part of the sphere 
of the term which is taken into the scope of the judg- 
ment by its undistributed use. We thus convert the^ 
indeterminate undistributed term into a determinate 
distributed one with a narrower and comprehended 
sphere. 

529. It is sometimes a matter of doubt whether a 
Modal shall be considered as belonging to the Subject 
or the Predicate of a Proposition. 



136 LOGIC. PART I. [chap 

It is not of so much importance to which it is con- 
sidered as belonging as might at first sight appear, as 

the Modal can easily be transferred from one 
Modl?^^ ^from tcrm to the other. Thus, "Drowning men 
diiatl?and v^ catcli at straws ; " — " Drowning " is here a 

Modal of the Subject. But if we say, " Men 
catch at straws when they are drowning^'^ the Modal 
is transferred to the Predicate, and the Proposition 
remains the same for all Logical purposes ; although 
that which was the differentia of a species in the sub- 
ject becomes the conditional of the genus in the Pre- 
dicate, and vice versa. 

530. We have yet another important class of Me- 
dals whose influence upon the deductive force of the 
protensire Formulac wc must consider. I mean those 
Modais. which indicate Protensive comprehension. 

531. Such Modais seem rather to limit the Copula 
than the terms of a judgment. 

532. It is obvious that when the Copulas in both 
the Premises are taken with unlimited Pretension — 

Absolute Pro- ^hat is, witli the adverb '' always " or " uni- 
tension. vcrsally " expressed or implied, we may 

have a Copula in the Conclusion with the same pro- 
tension. 

Let us then consider those adverbial Modais which 
limit the Pretension without giving a definite limit to 
it, such as " sometimes," '' generally," '' rarely," &c. 

533. It is manifest that such Modais always limit 
the Subject, so that a Proposition in which one of them 

Limited Pro- occurs cauuot bc regarded as universal. Nor 
tension. ^g ^j^jg ^\\ — ^j^^y indicate that there is no one 

part of the Subject of which as a species the Predicate 
may be affirmed with unlimited Pretension. It may 
^be affirmed of any or all the individuals included in 
the Subject at some time, and at others perhaps it can 
be affirmed of none of them. 

534. New if there is such a Medal in both Pre- 
in both Pre- i^iscs, it is mauifcst that we can have no 

mises. Conclusion. For example : 



ni.J OF SYLLOGISMS. SECT. VI. 137 

M is sometimes P. 
S is sometimes M. 



For it does not appear but that M may be included in 
P precisely then when S is not included in M, and 
vice versa. The Minor term may be included in the 
Middle when, and only when the Middle is not in- 
cluded in the Major term. 

535. But if the Modal is in either Premise alone it 
must be in the Conclusion also. For if either j^ ^^^ p^^. 
Subject is in its Predicate only sometimes, °"^®- 
then the Conclusion can affirm the Minor term to be in 
the Major only '' sometimes P And at any particular 
time it can predicate the Major of the Minor only in a 
Problematic or Probable Judgment. The Conclusion 
with such a Modal in either Premise, therefore, may 
assume either of the two following forms : 

S is sometimes P ; or 

S may be P ; 
that is, it may be so without contradiction or logical 
absurdity. 

536. We sometimes have a Protensive Modal, how- 
ever, when we ou2:ht to have a differential Protensive for 

J... T rn? Differential Mo- 

or conditional, inus : dai. 

" Testimony sometimes leads us into error. 

The belief in miracles rests upon testimony. 

Hence the belief in miracles may be only an error." 
Here for " testimony sometimes " we manifestly ought 
to have " some testimony ; '' that is, " some kinds of 
testimony misleads us." 

But when we substitute " some kinds of testimony," 
for '' testimony sometimes," we have not got the iull 
force of the Modal or the exact meaning of the Propo- 
sition. It does not mean to affirm that there are any 
kinds of testimony that always mislead. The Modal 
of the Copula must therefore be still retained in some 
other form. We may say, " some kinds of testimony 
occasionally mislead." 



138 LOGIC. PART I. [chap. 

SECTION VI. 

Of Comjpound Syllogisms or Sorites. 

537. The Syllogism gives us a Conclusion but one 
step further removed from the intuitive judgments 
than the Premises themselves, having but one Middle 
term. 

538. We may however have in the same Formula 
Sorites. any number of Middle terms with a deduction 
for a conclusion, of a corresponding degree of remote- 
ness from the Premises. Thus, 

AisB, 
BisO, 
OisD, 
.-.AisD. 
This is called a Sorites or Chain Syllogism. 

539. In the usual form the Predicate of each Prc- 
orderof Terms misc bccomcs thc subjcct of the next in a 
Form.^ ^"^^ Universal Affirmative Proposition, imtil in 
the Conclusion we have the subject of the first Premise 
for subject as Minor term, and the Predicate of the 
last for Predicate as Major term.^ 

540. In this Formula each successive term begin- 
ning with the Minor, has a wider and comprehending 
sphere until we come to the last. Consequently what- 
ever may be predicated of the last or Major term, may 
be predicated of the first or Minor term just the same 
as if there had been but one Middle term. 

541. It is manifest that as there can be but one 
One Minor Couclusion, SO there can be but* one Major 

Term?^ ^^^"^^ aiid but ouc MiuoT Premise. But there mav 

* A Sorites, called the Goclenian, has heen noticed also — consisting of 
Propositions in which the terms are arranged in the inverse order ; 

Thus B is A, 

C is B, 

Disc, 

EisD, 

.\ A is E. 

And this form with the usual form given ahove, are all that have hitherto 

been recognized so far as I know. 



in.J OF SYLLOGISMS. — SECT. VI. 139 

be any number of Intermediate Premises introduced 
between the Minor and the Major instead of intermediate 
one — each Premise introducing a new Mid- p^^emises. 
die term, until the last becomes with the Major term 
either the Subject or Predicate in the same Proposi- 
tion. Thus : 

All Z is A, 

All A is B, 

All B is C, 

All C is " 

All " is N", 

All N is X, 
.-. All Z is X. 

542. But there is no necessity for confining the 
Sorites within such narrow limits as have More than one 
usually been assigned to it. In fact we can- for™ of sorites, 
not keep it within these limits. Other forms and varie- 
ties are constantly occurring, and the business of Logic 
is rather to account for what is, than to determine 
what ought to be. 

543. It is obvious, that if we can introduce one 
Universal Affirmative between the Minor and Major 
Premise of any Syllogism, we can introduce any num- 
ber so long as the Subject of the one becomes the Pre- 
dicate of the next, or vice versa / in which case each 
new Middle term will be once distributed. 

544. Hence in any Syllogism, if after transposing 
the Premises, we can pass from the Minor Any syiiogism 
Premise to an Universal Affirmative and Sed. ^ 
from that again to the Major Premise, we may conti- 
nue on with any number of Universal Affirmative In- 
termediate Premises, without changing the essential 
character of the Sorites. 

545. In this way we find that each of the nineteen 
Syllogisms may be expanded into Sorites. 

546. In the expansion of the Syllogisms by this 
means we are to regard only the two Falla- cautions to be 
cies of Figure — Undistributed Middle and J-egaraed. 
Illicit Process. Each Middle term must be distributed 



140 LOGIC. — PART I. [chap. 

once, and no term distributed in the Conclusion which 
was not distributed in the Major or Minor Premise. 

547. It is sometimes the case that in the expansion 
of the Syllogism, we are obliged to resort to the inverse 
TheGocienian of tlic usual mcthod, or to what is called the 
Slnsion. ^ ^''' Goclenian method. Thus in the expansion 
of Camestres : 

N"o Z is A, 

All B is A, 

All C is B, 

All X is 0, 
.-. NoZisX; 
in which case the Subject of each Intermediate Pre- 
mise becomes the Predicate of the next, and the inverse 
method would give an illicit of the Major. 

548. The introduction of a Negative Intermediate 
Premise between two AflB:rmatives, or of a Particular 

A Negative betwccn two Univcrsals, will have its usual 
Intermediate, effccts upou the quantity and quality of the 
Conclusion. Thus Darapti expanded by a IsTegative 
Intermediate Premise becomes : 

All Y is Z, 
No Y is B, 
All B is X, 
.*. Some Z is not X. 

549. The Sorites may be resolved into as many 
int^o%'y1fogfsmr'^ Sylloglsms as it has Premises less one. 

550. The first Premise containing the Minor term 
of the Sorites is the Minor Premise of the first Syllo- 
gism, and the second Premise is the Major. The Con- 
clusion of the first Syllogism becomes the Minor Pre- 
mise, and the third Premise of the Sorites becomes the 
Major Premise of the second Syllogism, and so on, 
each Conclusion, becoming Minor Premise for the next 
Syllogism. 

551. In this way each Middle term after the first 
serves as a Major term to establish the Minor Pre- 
mise of the Syllogism in which it is to serve as a 
Middle. 



in. J OF SYLLOGISMS. — SECT. VI. 141 

Thus the most ordinary form of the Sorites is : 

All A is B, First Example. 

All B is C, 
All C is D, 
All D is E, 
.-. All A is E ; 
which is resolved into Syllogisms as follows : 
1st. 2d. 3d. 

All B is 0, All C is D, All D is E, 

All A is B, All A is 0, All A is D, 

.-. All A is 0, .-. All A is D, .-. All A is E. 
In this case each of the Syllogisms is in Barbara. 

552. For another example take the following : 

All O IS A, Second Exam- 

C is not D, p^^- 

All B is D, 
.-. Some A is not B ; which is resolved as 
follows : 1st. 2d. 

C is not D, All B is D, 

All C is A, Some A is not D, 

.-. Some A is not D. .*. Some A is not B. 
The first of these Syllogisms will at once be seen to 
be Felapton (3d Fig.), and the second is Baroko of the 
2d Fig. 

553. In most cases where Bramantip occurs in the 
course of resolving the Sorites into Syllo- ^he peculiarity 
gisms, it is necessary to use the indirect of Bramantip. 
Conclusion for the Minor Premise to the next Syllo- 
gism. Thus : All A is Z, 

All B is A, 

All N is B, 

All N is X, 

.-. Some Z is X. 

(1) All B is A, (2) All IT is B, (3) All N is X, 

All A is Z (ind. Con.) All B is Z, Some Z is N, 

.-. Some Z is B, .*. Some Z is "N^ .*. Some Z is X. 

The same thing occurs in Disamis, Bokardo, Braman- 
tip, Dimaris, &c. &c. 



14:3 LOGIC. PAUT I. ' [chap. 

554. In the statement of the Sorites, as in fact in 
the statement of the Syllogism, there is sometimes a 

Combination rhctorlcal complication of terms, by means 
BteSnt'" '^of of which the Subject is kept more constantly 
Sorites. before the mind than it could otherwise be. 

This is effected by converting each Proposition into a 
single cognition as we pass along according to the 
principle laid down [187]. Thus, 

" All men are mortal. 

All mortal men are sinners. 

Christ died for all sinful men. 
But the sinners for whom Christ died must exercise 
faith and repentance towards God in order to obtain 
the benefits of His death ; therefore those who do not 
believe in Him and live a life of faith and repentance, 
will be left to the full consequences of their sins." 

555. The only additional point to be secured in 
Caution against analyzing such arguments, is that no new 
matten^^^^ term be surreptitiously introduced by this 
process of accumulation. 



SECTION vn. 
Of the Incomplete Formula. 

556. For the most part in ordinary reasoning one 
Premise and sometimes two are suppressed ; that is, 
Premises often ^hcy are not stated in the course of the argu- 
suppressed. mcnt. The reason is often a rhetorical one. 
It would be tedious to be constantly repeating what is 
so obvious as to be known and admitted by all. Logic 
however never supposes any thing ; it requires all the 
Premises to be stated, and hence w^e must examine 
these abridged forms of argument. 

557. They are called Enthymemes^ and may be of 
Four kinds. four kiuds : 

(1.) When one Premise of a Syllogism is omitted. 
First. In this case we have the Conclusion and one 

Premise, but the Conclusion and the Premise contain 



m.] OF SYLLOGISMS. SECT. YH. 143 

only three distinct terms ; as. All Y is X, therefore All 
Z is X. 

(2.) We may have tTie Conclusion and one Premise 
with, four distinct terms ; as, All A is B, second, 

therefore All Z is X. In this case the Enthymeme is 
an abridgment of the Sorites, and the given Premise is 
the Middle Premise. 

(3.) Or there may be a Conclusion given with more 
than one Premise, and yet not a complete Third. 

Sorites. 

(4.) In the fourth case we may have several Pre- 
mises in which there is one term common to Fourth, 
them all. 

558. Enthymemes with three terms are easily com- 
pleted into Syllogisms. The Conclusion ne- completion of 
cessarily contains the Major and the Minor o^^th^^Tst 
terms. The given Premise contains the Mid- ^°^- 

die term and either the Minor or the Major term, and 
determines the position of the Middle term as Subject 
or Predicate of the given Premise. From this we learn 
the Figure, the quality and quantity of the Premise 
to be supplied. 

Thus, if the Conclusion be A, the Premises must 
be AA. 

If the Conclusion be E, the Premises must be either 
EA or AE. 

If the Conclusion be I, the Premises must be either 
AI or LA. — (AA of course would be valid but not 
necessary.) 

If the Conclusion be O, the Premises must be 
either EI, OA or AO. 

559. We must always remember that we have no 
right to supply a Universal Premise in the ^^ universal 
completion of an Enthymeme when a Parti- dS'^'unilsru 
cular one would answer. This would be ^^ necessary, 
attributing to him who made the Enthymeme what he 
never said and what his argument does not necessarily 
imply. For this reason no Enthymeme can require to 
be completed in Darapti, as Disamis and Datisi are in 



144: LOGIC. PAKT I. [CHAP. 

the same Figure, in one or the other of which any En- 
thymeme with a Conclusion in I in the 3d Figure can 
be completed. 

560. If it is found impossible to complete the Syl- 
logism — that is, to find a Premise that will connect the 
given Premise legitimately with the Conclusion, the 
Enthymeme includes or implies a fallacy which ren- 
ders its conclusion worthless or worse. 

561. Of Enthymemes with four terms there can be 
Enthymemes oulv the ouc Variety g-iven, except as the dif- 

with Four t} *^ . i'x 1 T^ 'i 

Terms. lerencc m quantity and quality may vary it : 

All A is B, 
.-. C is D. 
Any variation of the relative position of these terms 
would produce no variety in the Formulae. It could 
only change the term which a given letter represents. 

562. If an Enthymeme has four distinct terms, two 
of them must of course be Middle terms, and it can be 
Completed into complctcd iuto a Soritcs with three Pre- 
a sorites. niiscs ; thus, A is B, therefore C is D.— " The 
state punishes no man for his religious opinions, there- 
fore heresy is no crime." 

563. Here we have four distinct terms — " state," 
" religious opinions," " heresy," and " crime ; " and 
the latter of the two Propositions is given as a Conclu- 
sion from the former. Let us then put A for state, B for 
religious opinions, C for heresy, and D for crime, and 
we shall have : 

All C is B, 

No A is B, 

All D is A, 

No C is D, or C is not D. 

564. From which it appears that the Enthymeme 
implied the two following Propositions : 1st, the Minor 
Premise that all '' heresy "^^ is '^ religious ojnnion^'^ of 
some kind or another. — 2d, for the Major Premise 
whatever is a '' erime^^ is '' punished hy the stateP Or 
as for rhetorical purposes one would be most likely to 



in.] OF SYLLOGISMS. — SECT. vn. 145 

express the same thing by contra-position — " whatever 
is not punished by the state is no crime." 

565. But in the third case we may have the Con- 
clusion of a Sorites with two or more of the Enthymemes 
Premises given and others suppressed. four tSmf .^''^" 

566. A fundamental maxim in the completion of 
these Enthymematic Formulae, is that in no new terms 
completing them no term may be used that introduced. 
was not contained in the Elements of the Formulae that 
were actually given. 

If now we have — A is B, 
BisC, 
OisD, 
D is E, 
EisF, 
.-. A is F ; 
it is obvious that if the 1st, 3d, and 5th Premises were 
omitted, we should have all the terms given, A, B, C, 
D, E and F. Thus, B is C, 

D is E, 
.-. A is F, 
and we could easily restore the wanting Premises by 
principles with which we are already familiar. 

567. But if one Premise were stricken out or omit- 
ted, the full form could not be completed. We should 
have :— All B is C, j _ ) All D is E, 



A is F. 1 """^ f .-. All A 
which would be completed thus : 



1 



IS 



All A is B, 


or, All A is D, 


All B is C, 


All D is E, 


All C is F, 


All E is F, 


All A is F, 


.-. All A is F. 



568. As the Middle term is usually a general term, 
that is a term denoting a class, it is obvious Enthymemes 
that the result will be the same if in a sue- ^er%8tSi^ 
cession of Propositions we compare either of <iivi<i"aiiy. 
the Extreines with the individuals of which the Middle 
term is composed, as if we should compare that Ex- 

7 



146 LOGIC. — ^PAET I. [chap. 

treme with tlie Middle term as a Whole in a single 
ciassificatory Proposition, this gives a Glassijicatory For- 

Formula. mula. 

569. Thus let M be a genns consisting of the indivi- 
duals a^ J, c^ d and e^ we may thus predicate P of each 
of these ; as, ^ is P, 

h is P, 

G is P, 

d is P, 

^ is P ; 
and then as whatever may be predicated of all the 
individuals of a class, whether genus or species, may 
be predicated of the class, we may have for these seve- 
ral Propositions, M is P ; since by the supposition M 
is the general term whose comprehended individuals 
are a^ 5, c^ d and e. With " M is P " we may have 
the Conclusion S is P — the two constituting an Enthy- 
meme. 

570. This it will be seen by and by is the Form in 
The Formulas which luduction is usually stated ; thus, 

of Induction, thc wolf, the fox, the cat are individuals 
which make up, or at least represent the class of ani- 
mals called CanidcB^ or animals with canine teeth. 
Now we may say : 

The wolf is carniverous. 

The fox is carniverous, 

The cat is carniverous, 
/. the Canidse, or animals with canine teeth, are car- 
niverous. 

571. It will follow of course on the same principle, 
Cumulative ^hat if wc predicate the several individuals 

Formula. ^^f ^hJch thc Middle is composed of the Mi- 
nor term individually, we may predicate the Middle 
itself of that Minor, thus : 

S is (3^, 
S is J, 
S is c, 
S is <^, 
Therefore S is M. 



m.] OF SYLLOGISMS. — SECT. vn. 147 

572. This is the Formula of what is called the 
Cumulative Argument, 

573. The Cumulative Formula diflFers from the In- 
ductive in that the Cumulative Formula is an Enthy- 
meme with the Major Premise suppressed. 

Thus in Mr. Webster's argument in the case of the 
White murderers, we have : 

" The prisoner was at the place at the time of the 
murder. 

" He participated in the motives which led to the 
commission of the murder. 

" He owned and usually carried with him the 
weapon with which the murder was committed. 

" He shared in the means which were afterwards 
taken to divert attention from those who were actually 
engaged in committing the murder. 

.-. the prisoner is guilty." 

574. It will often happen, as in this case, that there 
is no one term in the language that will de- sometimes 
note the genus, which these several terms g^rttrmfbrthe 
predicated of the Subject taken as a Logical ^^^'^'^^^• 
Whole, would constitute. But whether there is such 
a term or not they must be considered as making such 
a Whole, and one too which may be predicated of the 
Minor in the Inductive Formula, and of which the 
Major term may be predicated in the Cumulative For- 
mula. In the case alluded to, Mr. Webster argued his 
Major Premise at some length ; thus, " Whoever was 
present when the murder was committed had a motive 
and the means for committing it, and subsequent to 
its commission, endeavored to foil all attempts at dis- 
covering the murderer, must be held guilty." Here 
plainly for want of a single term of which to predicate 
" guilty," he enumerates the individuals of which it is 
composed— in short describes its sphere. 

575. In both of the above-named Formulae it is 
necessary that the Premise which is thus Must enume- 
individually stated, should enumerate all ordinate parts." 
the coordinate parts of the Middle term as a Logical 



14:8 LOGIC. TA^T I. [chap. 

Whole, otherwise it is manifest that we may have an 
Undistributed Middle. 

SECTION VIII. 
Of JEpichirema. 

576. Besides the Sorites we have sometimes For- 
mulae in which there is a Proposition, which is redun- 
dant so far as the purposes of that Formula are con- 
cerned. These Formulae have been called Ejpichirema, 
The Propositions serve an important purpose, and are 
called either Pro-Syllogisms or Epi-Syllogisms. 

577. The Pro-Syllogism is a Proposition thrown in 
Pro- Syllogism, either before or after one of the Premises as 
a Premise to that Premise ; and of course, therefore, is 
a Premise which with the given Premise for a Conclu- 
sion constitutes an Enthymeme. For example : " Con- 
fidence in promises is essential to the intercourse of 
human life (because without it the greatest part of our 
conduct would proceed upon chance). But there could 
be no confidence in promises if men were not obliged 
to perform them ; therefore the obligation to perform 
promises is as essential as the intercourse of human 
life."— (P^%.) 

578. Here the Pro-Syllogism, which is thrown in to 
confirm the Major Proposition, is enclosed in the paren- 
thesis. 

Again, we sometimes have a Conclusion stated im- 
Epi-syiiogism. mediately after the Conclusion of a Formula, 
and to which the Conclusion of the Formula is designed 
to serve as a Premise. This is called an Evi-Syllogism, 

As, Y is X, 
ZisY, 
.-. Z is X, 
.-. Z is W, 
or .-. M is X. 

579. Here the Conclusion serves as a Premise to 
the Epi-Syllogism, and the two together are an Enthy- 
meme. 



in.] OF SYLLOGISMS. — SECT. IX. * 149 

SECTION IX. 

Of Compound Judgments in Syllogisms. 

580. We have seen in a previous Section how any 
compound Proposition may, for all the purposes of the 
Syllogistic Conclusion, be regarded as a simple Propo- 
sition with a Modal. 

581. Such a process of course implies that the Judg- 
ments into which the Compound Proposition may be 
resolved, are either all false or all true toge- ^jj the sim- 
ther. When they are thus regarded how- S!us/be!mri? 
ever as simple Propositions with Modals, false together. 
we proceed with them as though they neither contained 
or implied more than the one Judgment, and the law 
concerning Modals already stated must be observed. 

582. When either of the Premises is a Compound 
Proposition thus regarded as a simple one, 

the Conclusion may of course be a Com- compoundcfon^ 
pound of the same kind ; only that it will 
appear as a Modal Proposition containing one modified 
judgment. This Proposition may be again resolved 
back into its component simple judgments by the same 
process, though in the inverse order — as it has been 
resolved from a Compound into a simple Modal Propo- 
position. Thus, M is (X and P), 

SisM, 
.-. S is (X and P). 
But the Major Premises may be resolved into " M is 
X," and "M is P." So also the Conclusion into "S 
is X," and " S is P." 

583. But it is sometimes the case that the Conclu- 
sion depends upon only one of the simple oniy one of 
judgments contained or implied in the Com- u^|d"''i?i^'^oS2 
pound Proposition. In that case whether the ''^'^^• 
Compound be either copulative or discretive, we must 
treat the judgment which is not taken into the scope of 
the Syllogism in the Premises, as in no other way be- 
longing to it or affecting it. It is a mere rhetorical 
surplusage. 



150 LOGIC. — ^PART I. [chap. 

584. Causal Propositions are properly Enthymemes, 
Causal propo- Containing a Conclusion and one Premise. 

The Causal Judgment maybe regarded as 
merely a Pro-Syllogism, We may also regard it as a 
mere Modal ; thus, 

"Christians are \i2c^Yl hecause they have faith ; 

The early martyrs were Christians : 

.-. the early martyrs were happy hecause they had 
faith:' 

585. When the Major Premise is a Causal, if the 
Minor affirms the cause of any new Minor term, the 
Conclusion may affirm the Predicate of the Major Pre- 
mise of the new Minor term. Thus we may say : 

" Christians are content with their lot, hecause they 
have faith / 

The Early Martyrs had faith : 

.*. the Early Martyrs were content with their lot." 

586. Now if this Conclusion be not true, it must be 
either because the Minor Premise is a non vera (un- 
true), or because the main Proposition in the Major 
Premise, " Christians are content with their lot," is 
untrue ; or finally, because the cause assigned — " be- 
cause they have faith," is not the cause, is a non causa 

PRO CAUSA. 

587. The Discretive^ Exceptional^ and the Exclusive 
Discretives, Ex- Propositious, as has been seen, asrree in con- 

ceptionals, and , • . , ^ , , -, , r» 

Exciusives. taming or implying judgment oi one qua- 
lity while they express a judgment of another. These 
judgments have one term common to them both. The 
Exceptionals affirm the Predicate of the subject and 
deny it of all other subjects. The Exciusives include 
the subject in the Predicate and exclude all other sub- 
jects from it. The Discretives affirm one Predicate 
and deny another of the same subject. 

588. Hence these classes of Propositions may be 
regarded as negatives or affirmatives, according as we 
involve in our Syllogism the one or the other of the 
judgments contained in them. Thus for a Discretive : 



in.] OF SYLLOGISMS. SECT. X. 151 

A is B, but A is not C, 

S is A, S is A, 

.-. S is B, .'. S is not C. 
For an Exceptive take the following : 

" All races of men except the Anglo-Saxons have 
failed to sustain free Institutions ; Examples. 

The Canadians are Anglo-Saxons : 

.-. the Canadians have not failed, &c." — 
or with a Negative Minor Premise : 

" The Mexicans are not Anglo-Saxons ; 

.-. the Mexicans have failed, &c." 

In the first case the AflBrmative Judgment is used 
as Major Premise, and in the second the ]!^egative. 

589. Again, in the case of an Exclusive, we have 
the same phenomenon : 

" "Water is the only thing in the sea ; 
Fish live in the sea : 
.-. Fish live in the water." 

" Water is the only thing in the sea ; 
Hot-blooded animals do not live in water : 
.-. Hot-blooded animals do. not live in the sea." 
In the above examples we have an Affirmative 
Conclusion in the 2d Figure, and a Negative Conclusion 
with an Affirmative Major Premise in the 1st Figure. 

SECTION X. 

Of Comparative Syllogisms. 

590. It has been usual to regard Comparative Judg- 
ments as but Pure Categoricals with Modals. po^ce of mo- 
But the Modals of Comparative Judgments paJltiie sylS- 
exert an influence upon the Formulae essen- ^^'°^'- 
tially different from that of any class of Modals yet 
considered. Comparative Judgments, as already shown, 
are Formally different from any other ; and constitute 
a class by themselves with differentia peculiarly their 
own. 



152 LOGIC. — PART I. [chap. 

Thus we may have — ^M is P, 

S is greater than M, 
.'. S is greater than P. 
Here we have a Modal to the Middle term in the 
Minor Premise, and none to it in the Major. We 
have also a Modal to the Major term in the Conclu- 
sion and none in the Major Premise ; and yet we see 
at once that the Formula is valid. 

Again we may have different Modals in each Pre- 
mise, as : T is greater than X, 
Z is equal to Y, 
.'. Z is greater than X. 

591. Comparative Syllogisms are of three kinds : — 
Three kinds. (1) Simple Comparativcs in Continuous 
Quantity ; (2) Comparatives in which the difference 
of intensity is regarded as cause ; (3) Comparatives 
of time, place, manner, &c. 

I. Simple Comparatives. 

592. In Continuous Quantity the reasoning depends 
upon the following Axioms : 

(1.) Axiom of Equality. If any two things are 
First Axiom, cach cqual to one and the same third thing, 
they are equal to each other. Thus, If A and B are 
each equal to C, A and B are equal to each other. 

(2.) Axiom of Difference. If of any two things one 
Second Axiom, is greater and the other less than or equal 
to a common third, then the one is greater than the 
other. Thus, If A is greater than C, and B is equal 
with C, A is greater than B ; or if A is less than C, and 
B is equal with it, A is less than B. 

(3d.) If two terms are both either greater or less 
Third Axiom, than a common third term, no conclusion 
can be drawn concerning them by means of a compari- 
son with that third term. 

593. If, however, in cases coming under the last 
Application of Axiom wc iutroducc Discrete Quantity also, 

Discrete Quan- , 7 i ^ i 

tity. SO as to express how much greater or less 



in.] OF SYLLOGISMS. SECT. X. 153 

each of the terms compared are, than that with which 
they are compared, a conclusion can be drawn — thus, 
three is two less than five, and six is one more. Hence 
six is three more than three. 

The two terms of which we speak in these Axioms 
are the Extremes, Minor and Major, and the common 
third term is the Middle term. 

594. We shall greatly facilitate our examination 
of the Formulae of Continuous Quantity by introducing 
a method of notation somewhat similar to Explanation of 
Sir William Hamilton's, — in which we will ^'^°'- 
denote comparisons which imply the equality of the 
two Extremes of a Comparative Judgment, by parallel 
lines drawn between the Subject and the Predicate, as 
S = P, '' S is equal to P." Comparisons of Inequality 
will be denoted by the Convergent when the Subject 
is larger than the Predicate, and by the Divergent 
when it is the reverse. Thus, S r> P, '' S is larger 
than P ; " and S <r P, " S is smaller than P." 

595. The fact that Comparatives of Inequality are 
converted by transposition of terms and convergent ,& 
changing of the Comparative Modal for that gi^^S 'Sf 
which is in the same degree of comparison each other. 
as the other side of the Positive, is indicated by the 
fact that the Convergent and the Divergent are but the 
converse the one of the other. 

596. But the Indefinite Comparisons, as we have 
seen, afiirm only that the Subject is as great Notation of the 
as the Predicate. We might therefore al- i^^^finite. 
ways represent these Comparisons by the sign of 
equality — only remembering, however, that such Pro- 
positions cannot be converted. 

597. But as such a mode of notation may lead to 
confusion in some cases, it will be well to denote the 
Indefinite Comparisons by two straight lines crossing 
each other, thus H — . 

598. Now since in Comparisons of Equality the 
compared and the standard of the compari- comparisons 
son are equal to each other, it will follow of Equality. 



154 LOGIC. PART I. [chap. 

that if both, or all the Premises are Comparisons of 
this kind, all Moods and all Figures must be valid. 

1st, A = B, 2d, A = B, 3d, B = A, 4th, B = A, 

B = C, C = B, B = C, C = B, 

... A = C, .-. A = 0, .-. A = 0, .-. A = 0. 

599. But if both are Comparisons of Inequality, 
Of Inequality uuless thej cau be so converted or read as to 

e"s of the'^same comc iuto the Ist or 4th Figure, and of the 
intensity. ^ gamc intensity, there can be no Conclusion 
except by means of Discrete Quantity. Thus : 
2d, A>B, 3d, B<A, 

C>B, B<C. 

In both these cases the Premises offend against the 
Third Axiom. 

600. But if the intensity be unlike in the 2d or 3d 
Of opposite Figures we may have a Conclusion. In that 

case the Premise may be read either in 1st 
or 4th Figures, and so brought under the 2d Axiom — 
the Axiom of Inequality ; thus, 

A>B, 

C<B, 
becomes " A is greater than B," and " B is greater 
than C." Hence we may have the Conclusion " A is 
greater than C," or A ==> C. 

601. If the Premises are read in the 4th Figure, 
. Premises read the Couclusion wlll bc of the oppositc intcu- 
Figirl. "^""^ sity from that in the Premises, or, which is 
the same thing, the Conclusion here, as in Logical 
Quantity, will be the converse of that in the 1st Fi- 
gure ; thus,— 1st, M :> P, 4th, P <:r M, 

S >M, M<S, 

.-. S p-P, .-. S:>P. 

602. If the Premises are Comparisons of Inequality, 
Comparisons of and of oppositc intcnsitv, they must be read 

Inequality. . ,, r^\^ oJ tti* ii 

m the 2d or 3d Figure ; thus, 
1st, Mrr-P, and 4th, P :>M, 
^S <M, ^ ^ M<S, 

offend alike against the Third Axiom. 



m.] OF SYLLOGISMS. SECT. X. 165 

But 2d, M^>P, and 3d, P:>M, 

.-. S>P, .-. S<P. 

603. We have seen that the Indefinite Comparisons 
cannot be converted, and must always be indefinite Pre. 
regarded as Comparisons of greater intensity, "'^^^'• 
though it is very possible in any case that they are not 
so. Hence when such a Comparison occurs in such a 
place as not to fulfil the conditions of Figures just 
stated, we are obliged to regard the Conclusion as in- 
valid ; thus, Mr>P, 

S+-M, 
.-. S r>P is valid. 
But M<P, 

S H — M gives no Conclusion, as the compari- 
sons cannot be read so as to bring them under the 
Axiom of Inequality. We might indeed read thus : 
P>M,) (P^M, 
S +- M, PM S = M ; 
but that would not improve the matter at all so far as 
their conclusive force is concerned, for we could not 
determine the comparison between S and P. 

604. When but one Premise is a Comparative Judg- 
ment the Comparative may be regarded as a one premise 
Modal, and we may proceed as in pure cate- ^^l compara- 
goricals ; thus, 

A is greater than B, 
Cis A, 
.'. C is greater than B. 

II. Corriparative Syllogisms in which the intensity as a 
difference of intensity is regarded as a cause, 

605. As an instance take the following from Kos- 
suth's late speech in England on the War in the East : 

" Napoleon failed to conquer Russia ; 
But Napoleon was superior to the Allied Powers : 
Therefore the Allied Powers will fail to conquer 
Russia " (that is, if they pursue their present policy). 
In this case we have a Comparative Judgment for 



156 LOGIC. ^PART I. [chap 

the Minor Premise, in which the Minor and the Mid- 
dle terms are compared with reference to the intensity 
of some property which they have in common. In this 
case it is " military force.^^ But the Major term here 
Conclusion af- IS predicated of the Minor in the Conclusion, 
fJSind oTsilffi- ^<^t on the ground of any of the Dicta of the 
cient cause. Figurcs, but bccausc the property common 
to both of the terms of the Comparative Judgment is 
conceived to be the cause or reason why the Major 
term is predicated of the Middle in the Major Premise, 
and therefore the reason why it may be predicated of 
the Minor in the Conclusion. But this implies the ex- 
istence of that which is the cause of the Major term in 
the Minor also, and moreover that it exists in as great 
intensity at the least in the Minor term as in the Mid- 
dle. And this is affirmed by the Comparative Judg- 
ment which is the Minor Premise. 

606. In Syllogisms of this class the difference in 
intensity must be a real Cause, and one which neces- 
sarily implies the reality of the effect. 

m1S'ner!''time! ^H- ^^^ CompciTatives of manner^ time^ 
place, &c. jplace^ ratio^ c&c. 

607. These are all very simple, and are completed 
by expanding or explaining the Comparative Modal 
for the Minor Premise ; thus, 

The Boys are with their Father ; 
Their Father is in the city : 
.-. The Boys are in the city. 

A is to B as C is to D, 
But A is one half of B, 
.-. C is one half of D ; 

or, A is to B as C is to D, 
But A is the Father of B, 
.-. C is the Father of D. 

608. It will be observed, that in all these cases the 
7h?MajS?p?emfsi' Comparative is the Major Premise. 



in.] OF SYLLOGISMS. SECT. XI. 157 

609. We may also have an Indirect Conclusion ; 

The Boys are with their Father ; pamd?e'"syX: 
The Boys are in the city : sisms. 

.*. The Father is in the city. 



SECTION XL 

Of Probable Syllogisms. 

610. By the application of Discrete Quantity to the 
measure of Wholes in Continuous and Logical Quan- 
tity, we have a further modification of Formulae and 
some new principles and rules to consider. 

611. Arithmetic, Algebra, and the Calculus are but 
methods of calculation in Discrete Quantity. 

Ti.-*n i.i? -L. j.JxT_j. Calculations in 

It Will not 01 course be expected that we Discrete Quan- 
shall go into a discussion of the Rules and ^'^^" 
Formulae belonging to these Methods in this place. 

612. There are but two fundamental Axioms in 
Discrete Quantity. 

(1.) The sum of the parts of any whole is that 

whole itself.^ First Axiom. 

The usual statement that the sum of the " parts is 
equal to the whole," though true, belongs to Continu- 
ous rather than to Discrete Quantity. 

(2.) If from any whole a part be taken, the remain- 
der is such a part as that together with that second Axiom, 
which was taken from the whole, it will make the whole 
itself. 

* We do not say, " eqtml to that whole," for that would imply a want 
of identity in the terms or objects of the conceptions. We say that " a whole 
is equal to the sum of its parts " in Continuous Quantity, Geometry, &c. 
But in Arithmetic we say, " 3 times 4 is twelve," not " is equal to twelve." 
Units, as such, have no differentia — and sums or wholes differ only in the 
number of units which they contain. 

When, however, in Algebra and the Calculus, we use the sign of equality, 
and read our statements or Logical Propositions, " X is equal to A," it is 
because "X" and ^' A" stand for quantities which while they are equal to 
each other as quantities have other relations, which must be kept distinctly 
before the mind. 



168 LOGIC. PART I. [chap. 

The first is the Axiom of Addition^ and the last 
that of Subtraction. 

613. Where several equal parts are to be added 
together to make one whole, the shorter method of 
Multiplication is adopted, and when several equal 
parts are to be taken from any whole the method used 
is called Division. 

614. The Involution and Evolution of Roots, the 
Methods in Biuomial Theorem, Fractions, Indeterminate 

Calculation. Quantities, Logarithms, are all but short and 
convenient ways of finding values. 

But it is important for us to investigate in this place 
the efiect of the application of Discrete Quantity to 
Logical and Continuous Quantity. 

615. By introducing Discrete Quantity a Compara- 
Discrete Quan- tlvc Svllos^ism whicli ofifeuds a^iust the 

tity applied to mi • i a • i i • . i . ^ 

Continuous. Inird Axiom, by having the two extremes 
either both greater or both less than the Middle term, 
and which consequently can have no conclusion by a 
comparison of Continuous Quantity alone, comes to 
have a valid conclusion ; thus. 

Three is two less than five, 

Two is three less than five, 
.•. Two is one less than three. 

616. Again, we may have an application of Dis- 
crete Quantity to Propositions which are protensively 

ToProtensive quantified, so as to give a valid conclusion 
Quantity. |.q ^^^ ^^^^^ ^^^ havc uouc without it ; thus, 

The cars stop at Waterloo one half of the time ; 

The cars carry the mail three fourths of the time : 
.'. Some mail trains stop at Waterloo. 

617. The principle involved here is the same as 
To Logical that which controls the influence of Discrete 

^eraf'^^ ^" ^^' Quantity when applied to Logical Quantity 
in general. For example take the following : — At a 
certain extensive conflagration it is ascertained that. 

Three fourths of the buildings in a city were of brick ; 

One half of the buildings were destroyed : 
.'. Some brick buildings were destroyed. 



m.] OF SYLLOGISMS.— SECT. XI. 159 

618. When one of the Extremes is expressed in 
integral Discrete Quantity, it does not at all Extremes in 
modify the Formula, as in the following ex- ?i|y"®^® ^"^"" 
amples : 

All that were in the Ark with Noah were saved ; 

Eight human beings were in the Ark with Noah : 
.'. Eight human beings were saved. 

All terms in which Discrete Quantity is expressed 
by the numerals, indicating simply how many are in- 
cluded in the terms are undistributed. Abso- 
lute Whole belongs to Logical Quantity, and distribSe/^ 
it is a Whole which is not included as an alter- ^"^' 
nate genus in any more comprehensive Whole or Sphere. 
Infinite belongs to Continuous Quantity, such as GOD, 
Space, Eternity, &c. But in Discrete Quantity we 
know of no number so large that it may not be a part 
of a larger and more comprehensive Whole, therefore 
none which is absolute ; and of none so large that it 
may not be made larger by addition, and therefore 
none which is infinite. The Units have no properties 
by which they are distinguished as Individuals, or 
divided into Genera and Species. It is true that '' one 
man " has such properties, but not as " oneP It is only 
as " man " that he has differentia and peculiarities. 
Hence in Discrete Quantity there are no Logical 
Wholes. 

619, Since a term expressive of Discrete Quantity 
alone, as '' six," " ten," " fifteen," &c., can never be a 
distributed term, such a Middle term can 

11 ' 1 . TVT- , If the Middle 

never help us to any conclusion. JN or vet be merely dis- 

,-"■ 1 1 -r\' i /-\ Crete Quantity 

can any term measured by Discrete Quan- there can be no 
tity serve as a Middle term, unless it ex- 
presses the ratio of the number expressed to the Dis- 
crete Quantity of the Logical Whole denoted by the 
term. For example : 

Three men got on the cars at the station ; 

Three men were killed in the cars : 
.-. The men killed in the cars were the men v/ho got 
on at the station. 



160 LOGIC. — PART I. [chap. 

620. The fallacy is obvious. — Nor from this state- 
ment can we infer any thing of the amount of the pro- 
bability that any one of those who thus got on were 
among the killed. Nor should we gain any thing by 
using a much larger number for the Middle term. 

621. It is only, therefore, when the Discrete Quan- 
tity expresses the ratio of those included within the 

The Middle scopc of tlic judgment to the number of 
JitSaTatioor Individuals included in the Logical Whole 
a Fraction. dcuotcd by thc tcrm which this Discrete 
Quantity qualifies, that it can be available for the pur- 
poses of deduction. 

622. We shall greatly facilitate our understanding 
of the principles upon which the conclusiveness of these 

Method of Syllogisms depends, by resorting to Plouc- 
Notation. quct's Mcthod of Notation, or at least a 
modification of it. Let a line be drawn, which by its 
length will indicate the unit of which the Middle term 
is a fraction, and another directly under it, in each case 
denoting the amount of the fraction. 

623. Thus to take the example just given, let us 
denote the whole number of houses by a line, and then 

How many at dircctly uudcr it two lines more — the one 
least. ^j^Q ]^^if ^jj(j j^i^Q other three fourths as long. 

And since we wish to know whether any, and if so, 
the least part of the Minor term that is necessarily con- 
tained in the Major, we will j)lace one of the fractional 
lines even with the unit line at one end, and the other 
at the other ; thus, 

» i i i I whole number ; 
i I i i number of brick houses ; 

I i i number of houses burnt. 

624. The reason for placing the lines as above, will 
be obvious from the fact that for aught that appears 
to the contrary in our statement, all of the not-brick 
houses were burnt, and only so many of the brick 
houses burnt as are necessary to make up the one half; 
that is, that the two spheres "bii7mt^^ and "bricky^^ 



m.] OF SYLLOGISMS. — SECT. XI. 161 

are as far as possible opposite. Hence the distance by 
which the lower line overlaps the one above it, will be 
the least part of the Minor term '-^hurnt^'' which can 
possibly be included in the Major term " hrickP 

But the overlapping portion of the two lines is one 
third of the one and one half of the other. 

625. Assuming then the term " brick houses " for 
the Minor term, we have for conclusion : 

" One thirds at least, of the brick houses were 
burnt." 

Or taking " burnt " for the Minor term, we have : 
" One half, at least, of the burnt houses were brick." 

626. But if the two lines when thus placed did not 
overlap each other at all, there would be no assertive 
conclusion ; that is, we could not say positively that 
any of the burnt houses were brick, or that any of the 
brick houses were burnt. 

627. From the foregoing it is certain that unless 
the sum of the two fractional values used as gu^ of the 
Middle term is more than a unit, we have bf more'th^n a 
no conclusion. ^"^^• 

628. The Conclusion in these cases may be mea- 
sured in Discrete Quantity, ecivins: the pre- conclusion djs- 

, -u • i: • . iT 1 i.^i.1, X cretely quanti- 

cise number, which is the least that can sed. 
have been included in the Predicate of the Conclusion 
as above, or we may have the undistributed Subject in 
Logical Quantity, " Some brick houses were burnt." 

629. Or if we place the lines differently, we shall 
see how many at most could have been how many at 
burnt. °'**''- 



i i i i i whole number ; 
i i i i brick ; 

I i i burnt. 

630. We place the lines thus because it is possible 
that the two spheres, " burnt " and " brick," are co- 
incident to the extent of the comprehensiveness of the 
narrowest. 

631. From this it appears that if the Minor term 



162 LOGIC. — PART I. [chap. 

has a sphere less comprehensive than the Major it may 
be wholly included in it. 

632. Let us now pass on to consider the application 
of Discrete Quantity to the calculation of probabilities 
in Syllogisms. 

633. There are three distinct classes of cases in the 
Calculation of Probabilities, which we will consider as 
involving all the Logical Principles which belong to 
that interesting but intricate and complicated sub- 
ject. 

634. (1.) We will first consider the effect of Dis- 
crete Quantification, expressed in a ratio or a fraction 

One Probable ^f the uuits of the Middle term, when one 
Premise. prcmisc ouly is a fraction and the other is 

unity ; thus, 

All the houses in the city were brick ; 
One half the houses were burnt : 
.-. All the burnt houses were brick; — or con- 
verselj", One half the brick houses were burnt. 

And the quantity of the Conclusion will be the same 
Quantification as that of thc Majov Premise, as in the above 
sion/ ^°^"* examples. The two Conclusions from the 
first of these, as will be seen, results from our regard- 
ing the one Premise as Major in the one case, and the 
other in the other. 

635. (2.) The next class of cases are those in which 
Dependent thc Prcmiscs arc all probable, and several 

probabilities are dependent upon each other. 

636. Of these we have two kinds — {a) that in which 
we have several Premises, and the value of each is 
expressed in fractions of the common Middle term, 
as in the case just given : 

Three fourths of the houses were brick, 
One half of the houses were burnt ; 
and (b) that kind in which the value of each Premise 
(after the first) is expressed in fractions of the value of 
the preceding Premise. 

637. {a) The probability that any particular house 
is brick, when three fourths of the whole are brick, is of 



m.] OF SYLLOGISMS. SECT. XI. 163 

course three fourths. And the probability that any par- 
ticular house is burnt, when one half of the 

Ti T j»i? T_ii?i?i.i Ratio of Calcu- 

whole are burnt, is oi course one nan oi the lation in Frac- 
whole. As the number of houses that are mo"n "* mme 
of brick, and the number that are burnt are 
each of them separately less than the whole, the pro- 
bability that a brick house is burnt, or that a burnt 
house is brick, is of course less than the probability 
that any particular house is either brick — or burnt ; 
that is, the probability that any particular house is ioth 
brick and burnt, is less than that it is either separately. 

638. We have seen that the probability that any 
particular house was burnt, when one half were burnt, 
is one half of the whole. Now of course the probabi- 
lity that any burnt house was brick, is one half of the 
whole number of the brick houses. But the whole 
number of brick houses is three fourths of the whole, 
the probability therefore that a brick house was burnt 
is one half of three fourths, which is three eighths of 
the whole number of houses. 

639. The probability that any particular . The probabi- 
brick house was burnt, is of course the same change SamI 

,1 1 i? 1 • 1 1 i 1 i as the probable 

as the number oi brick houses that were number of fa- 

T 1 1 1 , vorable chan- 

probably burnt. ces. 

This results from the principles laid down concern- 
ing the effect of classification upon predication ; for 
each brick house is an individual, of which the brick 
houses burnt is the species. Hence whatever we may 
predicate of the individuals distributively, we may 
predicate of the species generally, and vice versa what- 
ever we may predicate of the species we may predicate 
of each individual. 

Or the point may be proved in another way, as 
follows : 

640. The probability that any one house was burnt, 
is the same as the probability that any other house 
was burnt ; so likewise the improbability, p,^^^^ nj^the- 
The probability that any house was brick, "^^ticauy. 

is as we have seen 3 : 1, three to one : again the pro- 



164 LOGIC. — PART I. [chap. 

bability that any one house was burnt is 1 : 1, one to 
one against it — that is, one half. Now that fraction 
which sustains the same ratio to the number of brick 
buildings in the city that the number of the burnt does 
to the whole is f ; thus i : 1 : : f : f — three eighths of 
the whole therefore must be the number of brick build- 
ings that were probably burnt. And if more than 
three eighths of the whole number were burnt from 
among the brick buildings, then it would follow that 
since a larger proportion of brick than of the non-brick 
were burnt, the probability of any particular brick 
houses having been burnt is greater than the probabi- 
lity that a non-brick house was burnt. 

641. (5) In the second class of cases we have suc- 
cessive Premises, in which the value of each is ex- 
pressed in fractional values of the preceding Premise, 
as a whole or unity. 

This Process implies the form of the Sorites already 
explained (554), in which each successive judgment 
expressed as a single cognition, becomes the subject to 
the one which follows. 

642. Thus, suppose that a battle has been fought, 
concerning which we have the following particulars : 

Ratio of cai- " TJiTce fouTtJis of thc mcu in the army were 
fhl^mSoYi'ln ill the engagement. One tenth oi the men 
preceding°pr^e^ that wcrc cugagcd iu the battle were miss- 
mise. jjjg ^^^ next morning, and one third of the 

missing were killed." What is the probability that 
any particular man was killed ? 

643. It is obvious that \ of yV ^^ those engaged 
were slain. But "those engaged" were only three 
fourths of the whole. Hence f of \ of ~ that jf o == t o 
were slain. 

644. And from the reasoning already given, the 
probability that any particular man was slain on the 
7aere general ground of probability, is -^^ or 1 : 39. 

645. If, however, we have any particular class of 
Special ^rounds mcu amoUff whom the individual concerning: 

ofProbabiUty. , ^ 1 1 i.' • • *^ 

whom we are makmg our calculation is m- 



m.J OF SYLLOGISMS. SECT. XI. 165 

eluded, and they are known to have been especially 
exposed, the probability of his being among the killed 
is rendered greater by the consideration of that parti- 
cular ground affecting the amount of the probability. 

64:6. (3.) We will next consider the several cases 
of independent probabilities : 

{a) We have a class of cases in which we have a 
probability in one Premise, and an improba- Probability and 
bility in another. In that case we have only cSSwned.'^'^^ 
to subtract the one from the other, and the remainder 
will be of the same kind as the largest Premise. 

64:7. But when we have a special improbability 
against an event to be combined with several proba- 
bilities in its favor, this special improbability must be 
computed by using its complement as a new proba- 
bility, to be multiplied in according to the principle in 
the last named class of cases. 

648. Suppose an individual to have belonged to a 
department of the army which is but slightly General proba- 
exposed, call this an improbability of f , then cid ^probX- 
the probability that one in that department ^^^^• 

will be among the killed, will be of course but just ^ 
of the probability resulting from the other probabili- 
ties 4 Q- >^ 4 ^^ T6" O"' 

{b) We will next consider the class of cases in. 
which the question is of one of several one of several 

7 • # 7 , chances in the 

chances zn the same- event. same event. 

649. Thus, the die has six sides, and therefore six 
chances for each throw, and each throw is an event in 
which there are chances. 

650. Now what is the probability that either of two, 
say the ace and the deuce^ will turn up in any ^atio of the 
single throw or event ? It is of course dou- calculation. 
ble the probability of any one side or chance i + i =i. 

651. This is easily proved by supposing the question 
to be, what is the probability that some one Proved 
of the six sides will fall up. By the rule i+i+i+i+ 
^ = 6 = 1 Qp certainty. 

652. But we know previous to any computation, that 
one of the six sides will fall uppermost at each throw. 



166 LOGIC. — PART I. [chap. 

653. Hence in all cases where we have to inquire 
what is the probability of some one of several chances 
in the same event, we may add the sum of probabili- 
ties of the several chances. 

654. These "several" must, however, be a part 
Several must of somc ouc wholc, or totalitv of chances, as 

be parts of the . . ' > ^i • j.i • 

same whole, occumng lu ouc cvcut, otherwisc their sum 
may amount to more than unity ; which is impossible. 
Thus, suppose we have three probabilities, not included 
in any such unity, they may be |, \^ ^, then i+i+i=Tl 
which is absurd. 

655. id) This brings us to the last class of cases 
One chance in which wc wiU cousidcr — uamelv, that in 

several events. i • i i_i j.* • • i 

which the question is concerning one chance 
in several events. 

656. Of these there are two kinds — (d 1st) where the 
Two kinds. events are in the same totality of chances ; 
and {d 2d) where they are in different totalities. 

657. {d 1st) For the simplest case in this kind, sup- 
Differentia of P^^^c wc havc the qucstiou, " What is the pro- 

the first. bability of throwing any particular number 

on a die in two different throws ? " 

658. The probability of its being up in the first 
throw or event is \ , and the independent probability 
of its being up in the second throw or event is also \ . 

659. Here the totality — the six sides of the die — is 
the same in both cases, the two throws are different 
events. 

660. {d 2d) But for a case of the second kind take 
the following : 

Two thirds of the pious are grave persons. 

Three fourths of the studious are grave persons. 
Here the different totalities are '' the pious " and 
Differentia of '' ^^^ studious," and the question is what is 
the second. ^\^q probability that one who is both '' pious '' 
and '^ studious " will be " grave." 

661. The principle or rule of calculation is the 
same in both of these varieties of this class of cases. 

662. And we have two distinct questions to con- 



m.] OF SYLLOGISMS.— SECT. XI. 167 

sider — (1) What will be tlie average of the probability 
of one chance in any given number of events ? jy^^ ^^^ ^^^^, 
and (2) What is that probability in any par- ^**°^- 
ticular case ? 

663. These questions are by no means the same. 
In any indefinitely large number of events, gy ^^ means 
it is evident that each side would be upper- *^^ ^^®- 
most — that is, each chance would happen just as often 
as any other one chance. Each side of the die there- 
fore would come up just one sixth of the whole num- 
ber of events. If now we divide this totality of events 
into pairs, then of course a given side would come 
uppermost just as often as before ; that is, 1 : 5 in the 
whole. But the probability of any s-iven 

.-, . ^ » ' ^ ^ J. Ratio of calcu- 

Side comms: up once m every pair ol events, lating the aver- 

*~^ ^ , , xi • J A ii age probability. 

on an average is one third as great as the 
probability of its coming up once in three times as 
many chances, or twice as great as that of its coming 
up in each chance ; that is, i+i=i. So if we divide 
the events into triplets, the probability of any given 
side on the average of an immense number of events 
is three times as great as in the single event, that is, 

14-1-4-1 = 1 

6 "^ 6 J^ 6 2* 

664:. Now in this way the fraction can amount to 
more than unity, for as there are but six sides 

I .r* 1 -I 2. ' ii 1 '^he result may 

or chances, so ii we ask what is the proba- be more than 
bility of ace, for instance, in sets of ten 
events, we have } taken ten times or If ; that is, ace 
will come up on an average more than once in every 
ten throws. Otherwise ace will not come up so 
often as some of the other sides. But if it does not 
then there is some special reason or ground of proba- 
bility, which is contrary to the supposition on which 
we started. 

Let us now consider the other question — what is 
the probability of any particular chance in a definite 
number of events. 

665. It certainly can make no difference whether 
the events are in the same totality of chances or not, 



168 LOGIC. ^PART I. [chap. 

since in the throw of the die, for instance, the probabi- 
. , lity of any particular side in each throw is 
whether the ccrtainlj just as independent of each and 
thrsame totli- evcrj othcr throw, as it is of the probability 
of the head side of a cent's coming up in any 
throw of the cent. 

666. We may therefore consider the two kinds of 
cases in the class which we have named above {d)^ as 
depending upon the same principle and requiring to 
be calculated by the same rule. 

'Now we have two conditions to fulfil : 

667. (1.) The probability of any chance in two events 
Two conditions must bc greater than it is in either one of 
°ist condition, thcm alouc ; thus the probability of the ace 
in two throws is greater than it is in one. 

668. And not only so, but the probability in any 
number of combined throws must be greater than that 
of the sum of all the throws excepting any one of 
them ; that is, two must be greater than any one in 
the two, three than any two in the three, four must be 
greater than any three in the four, and so on. 

669. (2.) The sum of the combined probability can 
2d condition, uever amount to anymore than unity — for 
by the very mode of reckoning probabilities they are but 
the fractions of unity. When therefore they amoimt to 
unity, they are no longer probabilities but a certainty, 
and there can be nothing beyond. 

670. Now in the case of the die, for instance, as 
there are six sides the probability of throwing any 
We cannot add particular side, say the ace^ at the first throw 
the fractions. ^quM bc 1 : 5. or }. And in six throws it 
would be i+i+^+^+i+i or jX6=l unity. And yet 
it is possible that the given side might not be thrown 
once in six times, or even in any greater number. There 
is a bare possibility that that side might not fall upper- 
most in a thousand times. Still, however, when the 
And yet cannot cvcut is far from the sum of the probabilities 
The^^m ofth^ (provided they keep within unity) in either 
probabilities, dircctiou — that is, greater or less ; it creates 



luj OF SYLLOGISMS. — SECT. XI. 169 

a presumption and finally the unhesitating belief that 
there is some special cause influencing the chances, as 
that a die is loaded. 

671. It appears therefore that we cannot calculate 
the probability by adding the value of each fraction, 
since that method would soon produce unity, and ex- 
ceed it even. 

672. Nor can we calculate it by multiplying the 
fractions. The value in each successive Pre- we cannot 
mise is not a fraction of that of the preced- Fractions. 
ing or of any other fraction. Each one is the fraction 
of a unity, and of a different unity, as the 1st and 2d 
throws in the first example, and " the pious," and '^ the 
studious" in the second. And besides the multipli- 
cation of the fractions would give us a constantly de- 
creasing probability, when obviously we ought to have 
an increasing one. 

673. If now instead of the probability in each Pre- 
mise we take its complement improbability. By means of 
and multiply them together as fractions, and iit?. ^°°^'^ 
then take the complement of that product for the pro- 
bability of the conclusion, we shall have a method 
answering exactly the demands of the case. 

674. Thus in the first case the probability of an ace 
in two throws is | and |, the complement is | and |, 
multiplying we have ||, and taking the complement 
we have \^ . In five throws it becomes f-ff j , in six 
mil, thus approaching but never reaching unity or 
absolute certainty.^ 

* For the gratification of those who would like to see this ia a more 
purely mathematical form I give the following demonstration. 

Let the probability of a particular chance in one event be — , and that 

o 

of the same chance in another event - , certainty being unity. The com- 

d 

bined probabilities can never be greater than unity, nor less than the sum 

of all minus any one of them. 

Now multiply the complement of -which is (1 — -) by the complement 

6 o 

8 



170 LOGIC. — PAET I. [chap. 

675. In the second case we have | , or i comple- 
ment in unity, and | , or i complement. Multiplying, 
we have | x ^ =j\ or j| probability that the man who 
is both '' studious " and " pious " is " grave." ^ 

SECTION XII. 

Of Conditional Syllogisms. 

676. We are not to consider all sentences stated in 
the conditional form as expressing a conditional judg- 

of — wMcli h (1 -^ — ) and we have ^ -^ -^— ^ as the comple- 

d d bd 

ment of the product, which is the comhined probahility. For as the nume- 
rator cannot be greater than 6c?, the fraction itself can never exceed 
unity. 

Again this fraction may be put under the form —~\- (1 — t) i> ^ quan- 

b d 

tity which can never be less than — . 

Now suppose that both independent probabilities are imity, then they 
are not probabilities ; they have no complements and so of course they 
cannot be multiphed. 

Again, suppose them to be indefinitely near to unity, then applying 
the doctrine of limits, they may be assumed as unity, and so will have 
no complements to be multiplied. 

In either case the fraction becomes — — or unity, that is 1 x 1=1. 

od 

But suppose the probability in each case to be as near to unity as the 
nearest assignable quantity, then by this rule the product of two such pro- 
babilities would be nearer than any assignable quantity or indefinitely near. 
We may pursue the demonstration in this way for every assignable value to 
the fraction. If therefore there is any other rule that will give the same 
result, it is not another but the same. But if it gives a different result it 
cannot be true. 

* I have taken no notice of the effect of cQfncurrence upon the probabili- 
ties ; this will be considered in the Chapter on Methods of Proof. But it 
will often happen that the concurrence of two very small probabilities will 
produce an amount of conviction but very Httle if any short of certainty. 
Thus, suppose two men whose veracity was nothing should come in and 
report to me a certain occurrence, the one after the other, and under such 
circumstances that I could know that there had been no coUusion between 
them — the strength of the combined testimony might be but very slight-— 
but the fact of their concurring without coUusion would be very convincing, 
and aU the more so, the more strange and unexpected the event which they 
narrate. 



m.] OF SYLLOaiSMS. SECT. XH. 171 

ment. It is often the case that statements are made 
in the hypothetical form where no logical ^^^ ^ii condi- 
dependence of one member upon the other coSdkonauSdg''- 
is intended. Thus, "If on the one hand "^^"^^• 
Greece failed by an excess of the popular element in 
its constitution, Eome on the other became purely a 
military despotism, the least favorable of all forms of 
government to popular liberty." Here manifestly 
the judgment concerning Rome is not intended to be 
made dependent upon the truth of that concerning 
Greece. We must regard the judgments therefore as 
being logically two entirely distinct categorical affirma- 
tions. 

677. Nor is it always the case where a Proposition 
is a Conditional Judgment that the deductive ^he conditi- 
force depends upon the peculiarities of the a°me?e'°MSai 
Conditional Judgment. premis^e^^^^''"'' 

As examples take the following : 

"Whatever comes from God is entitled to faith and 
obedience. 

If the Scriptures are not an imposture they came 
from God. 

.*. If they are not an imposture they are entitled to 
faith and obedience. 

Or thus : All Y is X, 

(KMisZ, A)isY, 

^ .-. (IfMisZ, A)isX. 

678. In this case the Conditional is merely the Mo- 
dal of the Minor Term, and is treated accordingly. 
The Premise is used as a Complex Categorical rather 
than as a Conditional. 

679. But when the Conditional Judgment conditional 
is used as such, it is the Major Premise, and jo" premise fn 
there are two ways of completing the For- sySogismt. 
mula. 

From the nature of Conditional Judgments it fol- 
lows that : 

(1.) If we affirm the Antecedent the Consequent 
cannot be denied. ^^""^^^L^" 



172 LOGIC. ^PART I. [chap. 

(2.) If we deny the Consequent the Antecedent 
must be false ; that is, the contradictory of the Ante- 
cedent must be true. 

680. Hence we may complete in what is called the 
Constructive Constvuctive Method^ or modus ponens^ by 

n{i^^l ^^' affirming the Antecedent for a Minor Pre- 
mise, and have the Consequent for a Conclusion ; 
thus. If A is B, A is C, 

But A is B, 
.-. A is C. 

681. Or secondly, we may complete the Formula 
Destructive iu the Destvuctive Method^ or modus tollens^^ 
mSe^. ^®" by using the contradictory of the Consequent 
for Minor Premise, and then we shall have the contra- 
dictory of the Antecedent for Conclusion ; thus, 

If A is B, CisD, 
But some C is not D, 
.'. Some A is not B. 

682. But by denying the Antecedent in simple 
conditionals we do not disprove the Consequent, nor 
by proving the Consequent do we prove the Ante- 
cedent. 

683. But the Conditional Proposition is sometimes 
Exclusive Con- Hiadc au Exclusivc Conditional by the inser- 
ditionais. ^^^ ()f a only," " alone," &c. 

684. The effect of this exclusive is to show that the 
Consequent can have no other Antecedent, and could 
not exist without the one given in the Conditional. 
Thus, " If the Trojans came into Italy contrary to the 
will of the gods, they would then alone have deserved 
punishment. 

But they did not come contrary to the will of the 
gods. 

.'. They do not deserve punishment." — Virg. ^n. 
X. 'SI. 

* The words ^^ posit" and ^^amote" have sometimes been used to ex- 
press these processes. Thus if we posit the Antecedent the Consequent 
must follow, and if we amote the Consequent the Antecedent must be 
false. 



m.] OF SYLLOGISMS. — SECT. XH. 173 

685. In this case by denying the Antecedent we 
disprove the Consequent. 

And if we affirm the Consequent we establish the 
Antecedent. 

They deserved punishment ; 

.-. They came into Italy contrary to the will of the 
gods. 

686. But without the Exclusive Modal we prove 
nothing; concerning; the Consequent by dis- no conclusion 

* Ai \ 1 1 . from the oppo- 

provmg the Antecedent. site Methods. 

687. This will be obvious by the following illustra- 
tion : — " If John has a fever he is sick." Hence if we 
prove the Antecedent, viz., that " John has a fever," 
the Consequent that " he is sick " will not be denied. 
But if we disprove the Antecedent and show that " he 
has not a fever," we have not proved that "he is not 
sick." He may be sick from some other disease. 

688. For the same reason, though operating in the 
inverse order, if w^e prove the Consequent we do not 
thereby prove the Antecedent ; that is, if we prove that 
" John is sick," we have not proved that " he has a 
fever ; " his ailment may be something else for aught 
that would need to appear in our argument. 

689. The whole force of Hypothetical reasoning in 
either method must depend upon the Se- The validity of 
quence. There must be some such connection deSenSr^upoS 
between the Consequent and the Antecedent ^^^ sequence. 
in the nature of things and independent of our volition, 
that the truth of the one follows from that of the 
other. 

690. But as we have already considered the Se- 
quence or ground of affirmation in Conditionals, we 
need not add any thing more concerning it ^ny Enthy- 
here except to make the remark that the fxpTelsS^on^ 
Premise of any Enthymeme may be made ^^^'o^aiiy. 
an Antecedent, and the Conclusion a Consequent in a 
Conditional Judgment, and then the other Premise will 
be the sequence ; thus, If M is P, S is P. 

Completing as before we have : 



174 LOGIC. ^PAET I. [chap. 

IfMisP/SisP, 

But M is P, 

.-. S is P. 

691. But regarding it as an Enthymeme, we have : 

MisP, 

S is Jf 5 
.-. S is P. 

692. In the same way, any Conditional by means 
through seiuence ^^ ^^s Sequeuce is converted into a Catego- 
hcais""^ ^^'"^°- rical Syllogism. 

693. It is sometimes the case that the Conclusion 
depends rather upon some modal of the general Se- 

Modified se- qncncc than upou the gcucral scqucncc itsclf. 

die," the general sequence is " all that have fevers 
die," which is non vera pro vera; the Sequence, there- 
fore, if there be one, must be found in some peculiarity 
of " John," to be expressed by a modal. The Sequence 
then would be, " All {suh modo) who have fevers die ; " 
the sub modo denoting the differentia of the class to 
which the subject of the Antecedent belongs. This 
modal, however, should always be stated either in the 
Antecedent, or by giving the Sequence stated in such 
a form as to clearly point it out. 

694. If the Conditional has four distinct terms, of 
Conditionals coursc the Scqucncc becomes double, and 

terms. "^""^ the Conditional as an Enthymeme is com- 
pleted into a Sorites. Thus, If A is B, C is D. 
And we complete thus, C is A, 

A is B, 

B is D, 

.-. C is D. 

695. In what is called the Covipound Conditional, 
it is necessary to prove all the Antecedents in order to 

Compound cstabHsh the Consequent. If, however, we 
Conditionals. (Jisprovc thc Couscqucnt, we show that some 
one or more of the Antecedents is untrue, without de- 
termining by the Formula which it is. 



m.] OF SYLLOaiSMS. SECT. XHI. 175 



696. This makes the Minor Premise a compound 
compulative categoric Proposition. Thus, 

If A is B,) y. y 

andlf CisDj ^'^"^• 
But A is B, and C is D, 
.-. E is F. 

697. In continuous Conditionals if we prove the 
first Antecedent all the rest will follow. continuous 
Thus, If A is B, C is D ;— If C is D, E is F ;— conditionals. 
If E is F, F is H, and so on ; since each Antecedent 
after the first is the Consequent of the preceding Con- 
ditional, it is established by that first Antecedent. 

And conversely, if we disprove the last Consequent 
we have disproved all the Antecedents. 

698. We may also have Conditionals with Disjunc- 
tive Consequents. Thus, " If grain is cheap conditionals 
it must be either because the crops are large, l^lf ^conse- 
the consumers are comparatively few, or the *^"^°^^- 
importations are extensive." 

699. Completing this Formula and we have a Dis- 
junctive Conclusion. Thus, 

If A is B, either C is D, or E is F, 

But A is B, 

.-. Either C is D, or E is F. 

700. But if we complete in the Destructive Method, 
we must deny all the members of the Disjunctive Con- 
sequent. Thus, 

If A is B, either C is D, or E is F, 
But neither is C, D, nor E, F, 
.-. Some A is not B. 

SECTION XIII. 
Of Disjunctive Syllogisms. 

701. It has sometimes been held that there are two 
classes of Disjunctive Judgments — the Divi- comprehensive 
sive and Comprehensive. Those which we DisjuncSv'^s!^® 
have already considered are the Comprehensive Dis- 
junctive Judgments. 



176 LOGIC. PART I. [chap. 

702. The Divisives are rather categorical judg- 
The Divisives mcnts, ill which the divided whole is one 

pourfd cate^- tcrm and the coordinate terms are the other. 
Thus, " All food is either vegetable or ani- 
mal." 

Bnt we willpostpone the consideration of the com- 
pletion of the Formula of this class until we have at- 
tended to the other, or the Comprehensive Disjunctives. 

703. We have already examined the Disjunctive 
Judgments. They affirm that one of two or more 
judgments contained in the Disjunctive Proposition 
must be true without at all indicating which that 
one is. 

704. But it is not always the case that the deduc- 
Deduction does^tion dcpcuds upou this opposition of the 

not always de- . t -r>v« • ,' -r* *i» 

pend upon the parts, whcu a Disiunctive x'roposition occurs 

Excluded Mid- ^ r» ^i t-» ^^ . rrn 

die. as one oi the Jrremises. ihus. 

Every conqueror is (either a hero or a villain) ; 
Caesar was a conqueror : 
/. Csesar was (either a hero or a villain). 
All Y is (either X or W), 
All Z is Y, 
.-. All Z is (either X or W). 
Or the Disjunctive may be the Minor : 
All Y is X, 
Either (Z or W) is Y, 
/. Either (Z or W) is X. 
Or finally, the Middle Term may be Disjunctive in 
one of the Premises. Thus, 

Gold, silver, and platina are malleable ; 
All precious metals, are either gold, silver, or pla- 
tina : 

.-. All precious metals are malleable. 

705. But in this case the Disjunctive Middle must 
enumerate all the coordinate parts, and in one Premise 
at least, as above, it must not appear as a Disjunctive. 

For if we say — Either gold, or silver, or platina 
Not Disjunctive is malleable — as Major, and then write 
Sises!" '^' the Minor as above, we should manifestly 



m.] OF SYLLOGISMS. — SECT. xm. 177 

have an undistributed Middle ; and we might have the 
following as all the truth there would be necessary in 
the Formula : 

Either gold, or silver, or platina is malleable ; 
(suppose it to be gold only that is malleable) : 

All precious metals are either gold, silver, or platina ; 
(suppose it to be silver and platina only that are pre- 
cious metals), and then manifestly we should have no 
Conclusion, for the Major term was compared with 
gold and the Minor with silver and platina. This is in 
fact what is always done in the fallacy of undistributed 
Middle. 

706. In all the above examples the judgment is not 
Disjunctive. It is merely a compound categorical 
judgment with a Disjunctive for either subject or pre- 
dicate as the case may be. 

707. We have seen that the ground of a Disjunc- 
tive Judgment properly so called, that is, a Compre- 
hensive Disjunctive, is the Excluded Middle. It will 
follow, therefore, that if we deny one of the members 
the other must be true. 

708. Hence in all Disjunctive Syllogisms the Dis- 
junctive Judgment is the Major Premise. Disjunctive 
For the Minor we have the Contradictory of J?^|?%m£t 
one of the Members, and for the Conclusion ^sVogSr'''^ 
the other Member. Thus, 

Either A is B, or A is C, 
But A is not B, 
.-. A is C. 

Or, Either A is B, or A is C, 
But A is not C, 
.-. A is B. 

709. This is called by the Scholastic writers the 
modus tollente ponens. p^nl^.*""'°'" 

710. But if the coordinate terms are also coordinate 
parts of the divided whole, and not merely ^odus ponente 
Alternate Species, we may also complete in ^"®°^- 

the TTiodus ponente tollens. 

8^ 



178 LOGIC. PART I. [chap. 

Thus Either A is B, or A is C, 
But A is B, 
.-. A is not 0. 

This is either gold or platinum ; 
It is platinum : 
.*. It is not gold. 
The validity of this Conclusion depends not upon 
The mode de- the simplc Excludcd Middle but upon the 
?is"ion"^^'^ ^'' law of Division, that no individual can be in 
more than one of the coordinate parts of any divided 
whole at the same time and in the same respect. 

711. When there are more than two members we 
More than two obtaiu ouly a compouud categorical Propo- 
members. gitiou for the first auswcr. Thus, 

Either A is C, or A is B, or A is D, 

But A is not 0, 
.-. Either A is B, or A is D. 

We may thus proceed with this as before, and then 
we shall get a simple categorical Conclusion. Thus, 
Either A is B, or C is D, 
But A is not B, 
.-. C is D. 

712. From the foregoing it will be seen that what 
Divisive Dis- arc callcd the Divisive Disjunctives, can be 

piSed^onir?y completed by a Discretive Catesrorical alone. 

Discretives. rpr ^ *^ <=> 

Thus, 

All A is either B or C, 
S is A but it is not B, 
.-. S is C ; 
that is, we must include the Subject of the Conclu- 
sion in the Subject of the Major Premise, which is the 
divided whole, and at the same time exclude it from 
all the parts except one, which one is predicated of 
the Subject of the Conclusion. 

713. Nor is the Method materially different when 
the divided whole is the Predicate instead of the Sub- 
ject in the Disjunctive. As, 



m.] OF SYLLOGISMS. SECT. XIV. 1Y9 

a 1) and c constitute M, 
S is M but not a^ 
.-. S is either h or c. 



SECTION XIV. 
Of the Dilemma. 

714. The Dilemma seldom needs or requires any 
completion. It differs from the Compound DUemma. 
Conditional in that its Antecedents bear such a relation 
to each other as to constitute an Excluded Middle, and 
therefore some one of them must be true. And as the 
Consequent may be predicated on either one of them 
alone, it is immaterial which of the Antecedents is 
denied, as its denial aflSrms the other. 

715. These Antecedents are sometimes called the 
horns of the Dilemma. memm^^ ^^® 

716. The Dilemma is often Complex by having 
several Antecedents one after another. 

Thus Demosthenes says : 

" If ^schines partook in the public rejoicing he is 
inconsistent. 

If he did not he is unpatriotic." 

717. But in all such cases there is a real Conse- 
quent in which all the Antecedents or series 

of Antecedents unite. The obvious Conse- totheTompfex 
quent in the above case is that therefore 
"^schines is unworthy of public favor and confidence." 
The Formula may be thus expressed : 

If A is B, A is C, But If A is C, I . . T. 
Or, If A is B, A isD, And If A is D, f ^ '^ -^• 

718. Hence we may say, " Whoever committed this 
fault is either too ignorant to be our guide or too dis- 
honest to be trusted — in either case he is unworthy of 
our confidence." 

Which we may represent thus : 

K A is B, A is not C, And If A is not C, ) A is not 
Or, If A is D, A is not E, And If A is not E, j F. 



180 LOGIC. PART I. [chap. 

719. The Dilemma is not imfrequently stated in an 
Dilemma stat- inverted form. Thus, If A is B, either A is 

Id form. "^^^' ' D, or A is F. "If he fails, it is because 
he is ignorant of his profession or inattentive to his 
duties." 

720. This may be regarded as an Enthymeme 
stated conditionally with a Disjunctive Conclusion, or 
a Major Term with a Disjunctive Modal similar to the 
instance already given, &c. Thus, 

All B is either D or F, 
AisB, 
.-. A is either D or F ; 
or in the other form. Either A is D, or A is F. 

721. It is not unfrequently the case that in stating 
the Dilemma, the Antecedents are alone stated in dis- 
junctive opposition to each other, and the Formula is 

of course nothing more, than a Disjunctive 
quent soSt Judp-mcut. But as the Consequent of the 

times omitted. . ,1 n 'ji i • i • j • 

truth of either member is so obvious, and is 
in fact suggested by the circumstances and the occa- 
sion, the statement is considered a Dilemma never- 
theless. Thus, " The Dilemma then presents itself to 
us anew : Either we must accept the doctrine of the 
t/ransmutatio7i of species and suppose that the organized 
species of one geological epoch were transmuted into 
those of another by some long-continued agency of 
natural causes ; or else we must believe in many suc- 
cessive acts of creation and extinction of species out of 
the common course of nature ; acts which therefore we 
may properly call marvellous." — {WhewelVs Indica- 
tions of the Creator^ p. 39.) 

Here we have the two members of a Disjunctive 
stated as a Dilemma, and so called ; the j&rst member 
is considered absurd and the second therefore as 
true. 

722. Another form of the Dilemma is sometimes 
Antecedents uscd ; iiamcly, ouc iu which two Antece- 

m^Mory co"nse- dcuts arc affirmed with contradictory Conse- 
quents, quents, from which it follows of course that 



m.J OF SYLLOaiSMS. SECT. XIV. 181 

one of the Antecedents must be false. Thus, '^ Lord 
Bacon opposed the English system of colonization ; " 
therefore, " If Lord Bacon was right, the English sys- 
tem of colonization is wrong." 

But if the English are right, their system of coloni- 
zation is not wrong ; therefore, If the English are right, 
Lord Bacon was not right. Or if Lord Bacon was 
right, the English are wrong. 



182 LOGIC. — TAJEiT I. [chap. 



CHAPTER IV, 



OF FALLACIES 



Y23. "We have already noticed the difference be- 
tween the Form and the Matter ^ of an Argument, and 
although the Analysis of Formula takes no 
thosS^'^in ^\he account of the Matter, and supposes that the 
orm a. Formulss are valid whatever may be the 
Matter, there are certain sources of error which a mere 
inspection of the Formulse will never reveal to us. 
These have been called Fallacies, It is not easy to 
collect and classify them all, and yet something of the 
kind is indispensable. 

724. A Fallacy may be defined in its broadest and 
general sense to be any fault or error in an argument, 

Fallacies de- ^7 mcaus of which it (1) fails to prove any 
^^^' thing ; or (2) the Conclusion which has been 

assigned to it ; or (3) the Conclusion which was de- 
manded by the occasion or end in view. 

725. It has been customary to divide Fallacies into 
four classes. — (1) Fallacies in Form ; (2) Fallacies in 

Divided into Dictiou ; (3) Fallacies in Matter ; and (4) 
four classes. Extra-Logical Fallacics. The differentia of 
these classes is not very distinctly given anywhere, 
nor are the specific names used with any great uni- 
formity or clearness. We may perhaps define each 
species as follows : 

* See Introduction, 14. 



IV.] OF FALLACIES. 183 

726. Fallacies are in Form when the Formula of- 
fends against any of the rules of the mere FaUaciesin 
Form, and is perceptible without any con- ^**'°*- 
sideration of the Matter of the Argument. Hence 
Fallacies in Form should rather be called Faults than 
Fallacies, and we shall so designate them hereafter ; 
and then a Fallacy will be that which has the appear- 
ance of a valid Form, and deceives by its appearance 
of being Y^iuiiless, It does not fail to fulfil caiied Faults. 
the formal conditions of a proof, but fails in the essen- 
tial conditions which lie beneath the Form. 

727. The fallacy may be said to be in Diction^ 
when the words in which it is stated are so Fallacies in 
used as to leave us in doubt as to the mean- Miction, 
ing, and in fact so as to have several meanings in the 
same Formula. 

728. The Fallacy may be considered as in the 
Matter^ when one Premise or both of them Fallacies in 
are taken in a sense not intended, or when ^^"®^- 
they fail to express the judgment adequately. 

729. And the Fallacy is extra Logical when it lies 
beyond the Province of Logic ; ^ as when it Extra Logical 
states as a Premise a Proposition which is ^aUacies. 
not true ; or proves a Conclusion, which though true 
enough, is not to the purpose. 

730. It is quite possible that an Argument should 
offend in more than one of these points at ^ore than one 
the same time. We must however remem- famf^ \xgn- 
ber that a Fallacy is simply a failure to °*^"'' 
prove. It does not necessarily follow that because the 
Formula contains a Fallacy therefore the Conclusion 
is false ; the Conclusion may be true after all, and all 
that can be inferred or predicated on the The effect of a 
ground of the Fallacy is simply that the Con- fallacy, 
elusion is not proved. But it is not (^^6'proved ; for 
disproof implies a concluding force in the Formula of 
which the Fallacy has deprived it. 

* See Introduction, 17. 



184 LOGIC. — PABT I. [chap. 

Including the JExt/t^a Logical we have seven distinct 
Enumeration Fallacics, cxcluding Faults in Form from 
of Fallacies, q^j. numbcr ; Ignoratio Elenchi^ Petitio 
Princvpii^ and the five in the use of the Middle Term.* 

* Akistotue [Soph. Elench.], and after him most other writers, reckons 
six Fallacies in Dictixme, and seven extra Dictionem, 

The six in Diction are : (1) Equivocaiion^ as " the dog is an animal, Si- 
nus [the star] is a dog, therefore Sirins is an animal ; " (2) AmphibolicB, as 
Sp' 5 dps, Tts, TovTo Spa, or as Aldrich gives it, Quod tangitur a Socrate iUud 
sentit ; Columna tangitur a Socrate : Ergo Columna sentit^ — the amphibology is 
in toOto, as beiog either accusative or nominative, and in the Latin exam- 
ple it is in the uncertainty as to the subject of sentit ; (3) Composition ; and 
(4) Division J as explained below ; (5) Accent ^ as when putting the accent on 
the wrong word, or the wrong syllable in a word, we give it a meaning 
different from that which was intended ; and (6) Figure of Speech, where on 
account of similarity of words one draws a false inference from one to the 
other, as because Musa is of the feminine gender therefore so is Poeta, 

The seven Fallacies extra Bictionem are: (V) Fallacy of Accidents ; and 
(2) a Dicto secundum quid ad dictum simplidter, as explained below ; (3) Igno- 
ratio Elenchi ; (4) A mm causa pro causa, whether it be a non vera pro vera, 
or a non tali pro tali. As an example of the first, Aldrich gives, *' A comet 
shines — therefore there will be war." This is a non causa, the comet being 
entirely innocent of causing wars. Of the second he gives, " Whatever 
will intoxicate is forbidden ; wine intoxicates, therefore wine is forbidden." 
" Not at all," he adds, '* but only the abuse of wine." Here wine is ad- 
mitted to be a cause of intoxication, but it is prohibited only when it is 
such, that is, in sufficient quantity as to cause intoxication ; (5) FaUacy of 
Consequences, as when a Conclusion is given which does not follow from the 
Premises — this in fact includes all Fallacies ia Form ; (6) Petitio Principii, 
when that is assumed as given which ought to have been proved ; and 
(7) the Fallacy of Plurium Interrogaiionum, when several questions are pro- 
posed as if they were one, which are yet so related to each other as to 
require dififerent answers. As, " Are honey and poison sweet ? Have you 
left off your bad habits ? " 

These thirteen Fallacies have been arranged into mnemonic lines ; 
thus, 

^QUIVOCAT. AMPHI. COMPONIT, DIVIDIT, ACC. FL 
ACCI. QUID. IGNORANS, NON CAUSA, CON. PETIT. INTERR. 

But I have preferred the classification given above in the text, for rea- 
sons I will not enumerate here ; the 1st, 2d, and 6th are included under 
Ambiguous Middle ; the 5th, Accerd, does not belong to Logic at all — at 
least it is a mere trick ; the same may be said of the 13th, Plurium Interro- 
gationum ; the 11th I have reckoned imder the head of Faults in Form; 
the 3d and 4th I have recognized by name, as also the 7th, 8th, and 9th ; 
the 10th, Nm Causa, I have included under the more general head of the 
Petitio Principiu 



IV.] OF FALLACIES. SECT. I. 186 

SECTION L 

Of the Ignoratio Elenchi^ or Mistaking the Issue. 

The words Ignoratio Elenchi mean " Ignorance of 
the Proof" which ought to be given, and ignoratio Eien- 
are applied equally to cases in which one is AiLraSthiS 
really and innocently ignorant, and to those ^FaUacy. 
in which one chooses to ignore the real issue to be met 
and the Proof necessary to meet it. In this view of it, 
therefore, it is not a Fallacy in Logic at all, but simply 
a fault in sagacity or honesty, or both. It is no fault 
in Form nor a fallacy in the use of Forms. It is no 
fault in Method, for the Formula and Method may 
both be faultless. It is therefore merely a failure to 
pursue the right End — a failure in Aim or End ; as 
disastrous of course to the success of an Argument as 
any fallacy can be, but differing in kind both from 
Fallacies in the uses of Formula and Faults in Me- 
thod. 

731. Nothing can be more important in the con- 
struction of an argument than a clear and importance of 
adequate conception of the precise point to the right End. 
be proved. Without this we may deceive ourselves 
or be imposed upon by others. 

732. The Ignoratio Elenchi^ or mistake of the Ques- 
tion, is more pernicious when it occurs in a where igmra- 

^ (* ^ , 1 , » tio \s likely to 

course oi reasomng where an argument is occur. 
introduced merely as subservient to some more general 
purpose or conclusion than elsewhere. In this case the 
deception is less likely to be detected, and the tempta- 
tion to it is much stronger than any where else. 

733. We have an illustration of this fallacy pointed 
out in the speech of Diodatus, given in Thucydides, in 
answer to Cleon, who had argued that it illustration from 
would be just to put the Mitylenians to Thucydides. 
death. Diodatus reminds him that that was not the 
question ; the question really before them was whe- 



186 LOGIC. — ^PABT I. [chap. 

ther it would be expedient for the Athenians in theii 
present circumstances to undertake it."^ 

734. Mistakes of this kind will be found on a careful 
^j^aiiacies of scrutiuj of far more frequent occurrence 
quent. '" '®' thau ouc would at first expect ; and nothing 
but the most careful scrutiny and the most sagacious 
discrimination of things similar in appearance, but dif- 
ferent in reality, can secure immunity from this kind 
of imposture. 

SECTION II. 

Of the Petitio Princvpii. 

Under this head I shall include all forms of assum- 
ing for Premises what ought not to be assumed, or used 
as such without being first proved to be true in the 
sense and to the extent used. 

735. Strictly speaking, the Petitio Principii is the 
Petitio princi- fault iu Mcthod which consists in stating as 
Suitin Method^ a Prcmisc a Proposition which contains the 
Conclusion, in such a way as that it can be evolved 
from the Premise by some of the processes of Imme- 
diate Inference. 

736. In the popular sense it means simply the 
The popular assumins* as true that which we are expect- 

sense of Ihe . • i • j i i t^ • i j 

word. mg or Wishing to nave proved, it is seldom 

the case that both Premises of an Argument are dis- 
puted or questioned, f and when the one that is thus 

* Thucydides, Book III, Year 5. 

t For this reason some writers, and writers on " Logic," even, have 
maintained that every Syllogism is a Petitio Princvpii, They cite such exam- 
ples as the following : 

All men are mortal ; 
John Smith is a man : 
.*. John Smith is mortal. 
But, say they, the Major cannot he affirmed as true unless John Smith 
he mortal. They forget that they heg the question themselves — the ques- 
tion, to wit, whether John Smith is a man or not. 

Let us take a case in which hoth Premises admit of douht, or are at 
least denied : 



IV.] OF FALLACIES. SECT. U. 187 

questioned is assumed, the assumption is regarded as a 
begging of the principle or main Premise on which 
the Conclusion depends. 

737. We have several forms of Premises unduly 
assumed, or untrue. We must, however, distinguish 
between a fallacy and a falsehood, or mere ^^^^.^ ^^ 
false statement. It is no part of Logic to miLsnotaFat 
ascertain whether Propositions introduced 
as Premises are true or false ; thus, If a man aflSrms 
that A is B, when it is not .so, the false statement is 
not a Fallacy for Logic to correct ; but it is a misstate- 
ment to be corrected by investigation into the subject 
matter of the Proposition.*^ The truth is to be sought in 

No murderer hath eternal life ; 
All warriors are murderers : 
Therefore No warrior hath eternal life. 

Here we have a Major Premise which some professing Christians deny, 
and others would of course deny the Minor. Hence in the estimation of some 
persons one Premise might be aflBrmed without involviag the truth of the 
Conclusion, and in the estimation of another class the other Premise might 
be afllrmed without involving its truth. In this case, therefore, neither Pre- 
mise can be regarded as a Petitio Principii. But this differs from others 
so far as this poiat is concerned, only in the purely accidental fact, that 
either one of its Premises are such as to be denied or doubted by any body. 

* It certainly diminishes our reverence for Aristotle immensely, to 
find that in his Prior Analytics^ Book II, he has devoted three chapters, II, 
III, and IV, to the consideration of the cases and conditions in which we 
may have a true Conclusion from False Premises ! If one could, he would 
disbelieve that these chapters ever came from the Stagyrite. But there is 
no help for it that I can see ; I find no intimation of their spuriousness. 

That there may be no mistake about the matter, and that the reader 
may see what cases the Father of Logic is discussing, I will give an exam- 
ple : "As animal is with no stone, nor stone present with any man, yet if 
animal is predicated of stone, and stone of man, we shall yet have the Con- 
clusion, man is an animal." Thus, 

" Every stone is an animal ; 
Every man is a stone : 
.*. Every man is an animal." 

The Conclusion is imdoubtedly true ; and it isyhwi, and a good waysyVoTTz, 
the Premises too. We might just all well substitute ^'' jack-hnife^' for Minor 
term, and prove by the same formula that a "jack-knife" is a man. 

It is no wonder that Logic has fallen into disrepute when we find the 
Father of the Science indulging in such ridiculous nonsense. Had this 
acutest of men got bewildered with the intricacy of his .own system, aban- 



188 LOGIC. — PART I. [chap. 

History, in Science, in Observation, &c. &c. The whole 
reahn of knowledge is to be put in requisition to deter- 
mine the truth or falsehood of Propositions when used 
as Premises. Logic is responsible only for the truth of 
the Conclusion on condition that the Premises are true. 
The assumptions under this head are reckoned by 
sumptions^ ^'' ^^^ c>ld wrltcrs as two : 

738. (1.) A nan vera causa pro vera causa. As 
when we say, " There is a comet, therefore there will 
be a pestilence." The completion of this Enthymeme 

Non vera pro wouild imply the asscrtiou, that "comets 
^^'^- cause pestilence," or " whenever there is a 

comet there is a pestilence ; " the latter of which 
statements is simply untrue, the former assigning for a 
cause that which is not a cause of the effect. Hence 
a non vera pro vera^ as it is usually written (omitting 
the word causd)^ is stating as a Premise that which is 
untrue. 

739. (2.) A non tali [causa] pro tali {causd?^ As, 
" Whatever is poisonous should never be taken. But 

NontaUpro opium is poisouous." lu this case it is ad- 
^^* mitted that opium is poisonous — that it is a 

cause of death, hut a cause of death only when taken 
in certain quantities or in certain ways. 
To these we may add one or two others : 

740. (1) When in categorical Premises the two 
relate to different points of time, as, " He who is most 

hungry eats most. But he that eats most is 
of Fafse ** A^^ Icast huugry, therefore he that is most hun- 
sumpuons. ^^ .^ least huugry." These Premises refer 
to different points of time in relation to the act of 
eating ; (2) then we may have want of sequence in 
Conditionals ; (3) non-exclusion of Middle in Disjunc- 
tives ; (4) want of sameness in kind in things compared 
in Comparatives. 

doned his a priori light, and set himself to justify by hook or by crook, as 
best he could, every possible Formula to which a Conclusion which is true as 
an independent Proposition, though not as a Conclusion, might be attached ? 
It would seem so. 



IV.] OF FALLACIES. — SECT. HI. 189 

SECTION IIL 

Of Ambiguous Middle. 

741. Not only must the Middle Term be once taken 
as a Whole, but it must be used in both Pre- Ambiguous 
mises in the same sense ; otherwise we have kiddie, 
the Fallacy in Diction of Ambiguous Middle. 

742. A word may be equivocal in itself, or intrin- 
sically, as in fact many words are, so that ^^^ds intrinsic- 
we really do not know precisely what one ^^^ ambiguous, 
intends by his Proposition, until we have heard him 
discourse long enough to render his terms perspicuous. 
Thus if one were speaking of "heat" in a scientific 
treatise, we should be in doubt whether by the word 
he meant that specific heat which is perceptible to the 
senses, or that latent heat which exists in all bodies to 
a greater or less extent and yet produces no eflfects 
upon the thermometer. And yet a Proposition might 
be true or false as the term was used in one or another 
of these senses. 

743. But if the Middle Term is taken in a different 
sense in each Premise, it is the same so far T^e Middle 
as all purposes of deduction are concerned, bJu'SuXlTe 
as if these were two entirely unlike and dif- Sie Termr 
ferent terms. 

744. " It is worth observing," says Whately,^ "that 
the words whose ambiguity is the most fre- ^pr^g ^,hose 
quently overlooked, and is productive of the ZstlveSenti? 
greatest amount of confusion of thought and overlooked, 
fallacy are among the commonest^ and are those of 
whose meaning the generality consider there is the 
least room to doubt. It is indeed from these very cir- 
cumstances that the danger arises ; words in very 
common use are both the most liable from the loose- 
ness of ordinary discourse, to slide from one sense into 

* Appendix, No. I. 



190 LOGIC. — PART I. [chap. 

another, and also the least likely to have that ambi- 
guity suspected." 

745. The Archbishop has collected some forty or 
.Habitual cau- fifty words illustrative of the foregoing re- 
Sgu^a'Jd. **"^ mark. But its truth and force can be appre- 
ciated only after a long-continued habit of carefully 
noticing the meaning of words as they are used in 
ordinary conversation and in the printed works, espe- 
cially those of a controversial character. A large part 
of all the controversy that has ever existed in the world 
has risen from persons calling the same thing by dif- 
ferent names, or by their meaning very different things 
when they use the same name or term. 

746. The Fallacy of Ambiguous Middle is spoken 
Several varie- of lu scvcral diflfercnt ways, but it is in all 

ties o am igui- ^j^^g^ classcs (if wc arc to regard these dif- 
ferent names as indicating different classes) essentially 
the same. Thus we have the Fallacy oi Equivocation 
when the same word is used in different senses. The 
Fallacy of Amphibology when the word is used so as to 
admit of different senses in each Premise. The Fallacy 
of Figure of Speech when the Middle Term is used 
metaphorically in one Premise ; and the Fallacy of 
Paronomasia &c. 

SECTION IV. 

Of the Fallacy of Division and Composition. 

747. This Fallacy consists in using the Middle Term 
in one Premise as a General Term, and in the other as 
a Collective Term. 

If now we use the Middle Term as a Collective 
Fallacy of Divi- Tcmi in the Major, and as a General Term 
"^°- in the Minor Premise, we have the Fallacy 

of Division / thus. 

The Komans [collectively] destroyed Carthage ; 

Brutus was a Koman [that is, belonged to the Ge- 
nus Poman] : 

/.Brutus destroyed Carthage. 



rV.] OF FALLACIES. — SECT. V. 191 

748. But if the Middle Term is used generally, or as 
a General Term in the Major Premise, and Faiiacyofcom- 
coUectively, or as a Collective Term in the position. 
Minor, we have what is called the Fallacy of Compo- 
sition ; thus, 

Three and two are two numbers ; 
Five is two and three [collectively] : 
.-. Five is two numbers. 

749. " This is a Fallacy with which men are ex- 
ceedingly apt to deceive themselves," says Whately ; 
" for when a multitude of particulars are presented to 
the mind, many are too weak or too indolent to take a 
comprehensive view, but confine their atten- ^he spend 
tion to each single point by turns and thus *^"^'^ Fallacy, 
decide, infer, and act accordingly. For example, the 
imprudent spendthrift finding that he cannot afford a 
certain great expenditure as a whole, resolves upon 
each of its parts separately, forgetting that all of them 
together will ruin him." 

SECTION V. 
Fallacy of Accidents and of Quid. 

750. The first, Fallacia Accidentis^ occurs when- 
ever in the course of the syllogism a term paiiacy of 
has been predicated of another, in reference Occidents. 

to its essential and inseparable properties, and taken 
as predicated of its separable accidents.^ 

What we buy in the market we eat ; 

We buy raw meat in the market : 
/. Eaw meat is what we eat ; or, " we eat raw meat." 

Here the Middle Term is predicated of the Minor 
essentially, and thus by means of the Middle Term the 
Major is predicated of the Minor, as if the Middle had 
been predicated of the Accidents rather than the Es- 
sentia of the Minor. 

* See Chap. II., 220. 



192 LOGIC. — ^PAET I. [chap. 

751. The Fallacy, a dicto secundum quid ad dictum 
simj[)liciter^ called for the sake of brevity the Fallacy 

FaUacy of ^^ Quid^ Is that ill which the Middle Term 
^"^- is taken in one Premise as used in its broad- 

est signification, and in the other as used only with 
reference to some special subject or application. 

As for example, when it is inferred from the decla- 
rations concerning the Virgin Mary, that she was pure 
and immaculate [as a virgin], that therefore she was 
sinless [as an accountable being], and so must have 
been born without any taint of human depravity. 

But the pureness and immaculateness as to virginity 
is one thing and absolute purity is quite another, and 
cannot be inferred from it. The fallacy is precisely 
the same as that made by the passenger in a railroad 
car when on seeing the notice, " No smoking allowed 
here," he inferred that the stove would not smoke. 

As another illustration take the following : 

Nebuchadnezzar ate grass like the oxen ; 
But the oxen eat grass standing on hoofs and 
chewing the cud : 
.'. Nebuchadnezzar had hoofs and chewed the cud. 

752. This Fallacy it will be seen arises from a dis- 
Most assertions regard of the scope and design of a writer. 
sL^pe. '" ^ ^^"^ In fact it is but seldom that any proposition is 
affirmed except when there is some special end in view, 
or some special object before the mind in reference to 
which it is true ; while in an application to objects of 
another class it might be entirely false. 

753. Besides the foregoing Fallacies, Whately has 
enumerated several others which are merely Tricks of 
the Rhetorician's Art, and the consideration of which 
does not belong to a Treatise on Logic. 

We have defined Faults as failures to fulfil the 

Formal conditions of an Argument, and Fallacies 

Tricks as dif- ^s failurcs to fulfil the Essential conditions 

Fad£ or £eJ2 Iji^^g bcncath the mere form. But a Ti-ick 

Fallacies. jg something which fails to be a Fault even. 



IV.] OF FALLACIES. ^SECT. V. 193 

A Fault can always be reduced to some Formula, one 
of the sixty-four Moods, though an invalid one. But 
a mere Trick has not the elements to complete any 
Formula. It cannot be put into the form or shape of 
an Argument, however successful it may sometimes 
prove in carrying a point and producing the legitimate 
results of sound reasoning. 



PART 11. 

OF LOGICAL METHODS 



CHAPTEE I. 

OF THE ELEMENTS OF METHOD. 
SECTION I. 

Of Method in General. 

Y54. Method is the way in which the means to any 
Method defined, end are used for its accomplishment. Con- 
sequently Method always supposes an End or object 
in view. Matter in which it is to be accomplished. 

Supposes an Mcaus to bc uscd iu its accomplishment, 
and Means. "^^ and au Agcut to usc them ; — the word is 
from the Greek /-te^* oh)v. Thus if I wish to be in a 
neighboring village, the road by which I go thither is 
my Method, while the carriage in which I ride, or 
my feet if I walk, are the Means which I use by the 
way. 

Y55. Method itself, however, may be resolved into 
several elements ; as, (1) Method, properly so called. 

Elements of that is, the Way by which one sliall go, as 
Method. jj^ going from one place to another ; (2) the 

Order in which the several steps shall be taken, as 
which first, and which next, and so on ; and (3) the 
Manner in which each step shall be taken. In going 



CHAP. I.] OF THE ELEMENTS OF METHOD. SECT. I. 195 

to a neighboring village there is no room for choice, 
as to which step shall be taken first in order, but one 
might take it into his head to walk sideways or back- 
wards. In this case his Method and Order might be 
perfectly good, but his Manner would be very awk- 
ward. In a general sense, however, all three of these 
elements are included in Method ; and Order and Man- 
ner themselves become but the Method of the subordi- 
nate parts of any whole with reference to which the 
word Method is used. 

756. Method gives unity of plan and efficiency in 
the use of means towards the attainment of Method gives 
any end. It is not always the strongest man cilncy^" 
that can accomplish the most work in a given time, 
nor the fleetest of foot that can make the quickest race. 
Inferior force is often rendered the most efficient by 
the superiority of Method. Method has to do with 
every thing. Method is the result of mental power 
and application. It indicates capacity and attention, 
as its absence indicates the want of them. 

757. Hence Method must form an essential part 
of any trade or art that is to be learned. It Method is the 
is in fact the conversion of Science into Art, knowledge *to 
the passing from knowledge to practice. practice. 

758. The beauty of any operation depends upon 
the Order and Method pursued in it, and the Beauty of ope- 

-i ,1 . • . 1 1 • 1 ration depends 

pleasure or the pam with which any accom- upon Method. 
plished performer in any department of human activity 
watches the acts of another depends upon the presence 
or absence of Method in the operator. And a quick 
insight into the Method of any act or series of actions 
is called genius for that kind of actions. 

759. In writing or speaking, not only the order in 
which the sentences follow one another, but . Force of writ- 
also that in which the words are placed minrr deS 
relatively to each other in each sentence, tK. 
depends upon Method ; and upon this arrangement 
depends the beauty and force of what is said or writ- 
ten. In a mathematical demonstration there is a cer- 



196 LOGIC. — vART n. [chap. 

tain method or order in wMcli the steps should be 
taken — and we should hardly call that a demonstra- 
tion, which although it had included all that was 
necessary, had thrown the parts together in entire 
disregard of the order in which they ought to follow 
each other. Such a demonstration, if demonstration it 
could be called, would demonstrate the want of capa- 
city in the demonstrator rather than the truth of the 
Proposition to be proved. 



SECTION 11. 
Of Order as an Ele7)ient of Method. 

760. Method always implies an End, and yet it is 
not concerned in the selection of that End. It is con- 
Ends deter- ccmcd merely with its attainment. The 

Si"!ty and^by End may be determined for us, or we may 
Choice. \yQ jgf^ ^Q choose it for ourselves. Ethics 

determine Ends for us when it specifies certain acts as 
being of moral obligation, and which therefore we are 
not at liberty to do otherwise than pursue. Theology 
determines Ends for us by showing acts which by 
the Will and Command of God are obligatory upon 
us. Polity determines Ends for us, as when the State 
commands certain acts by its positive enactments. 
Necessity determines Ends for us when by a fixed law 
of our nature it is ordained that we must eat to live, 
and must work in order to have something to eat. 
But in regard to many of our acts we are left to select 
our Ends for ourselves, as Pleasure, or Interest, or 
Benevolence may incline us. 

761. Order, however, is an important element in 
Order neces' Mctliod, and thcrc cau be no Method with- 

thSd. ^ ^" out Order. The Principles of Order how- 
ever are very few and simple, and the same in all 
departments of human activity. Always there is a 
place to begin, a place to end, and intermediate steps 
to be arranged. That step or act which presupposes 



I.] OF THE ELEMENTS OF METHOD. SECT. H. 197 

others cannot well be taken first, and that which is 
necessary to the succeeding cannot well be order to some 
postponed to the last. The mason cannot ^l^^^ ^^^^^l: 
lay the wall until the stone, and lime, and '^^^^'^y- 
sand have been drawn and the mortar made. The 
carpenter cannot dress the timber and fit each piece 
to its place, until the trees have been felled and the 
boards hauled to the place where they are to be used. 
So in studies — the alphabet must be learned first, 
geometry must be learned before trigonometry, and 
grammar before rhetoric ; and he that should under- 
take the calculus before algebra, or history before he 
knew any thing of geography, would find that he had 
made a mistake in Method, which would render all his 
studies and his efforts unavailing. 

Y62. That fault in Method which consists in invert- 
ing the true order of the steps, or successive The Fault of 
acts in any series of actions, has been called ^^^^^--^rst. 
by the Greek writers a va-repov irpSyrov^ that is, a later- 
f/rst. 

763. In every process there are some of the steps 
or elements whose position is fixed by the very nature 
and necessities of the case. Thus in the 

,. i? 1 ii, J. • 1 i 1 The Order of 

erection oi a house the materials must be many steps leit 
hauled to the spot before the walls can be ** ^ **^^^' 
put up. But in every process also there is a large 
number of elements or steps, the position of which is 
not so determined by the nature and necessities of the 
case as that there may not be varieties in the order ; 
and their disposal furnishes a sphere for the exercise 
of tact and genius. 

764. The five great Canons of Order are : of order. ^°°"^ 
(1.) Place that first which presupposes nothing as 

having preceded it. 

(2.) Put that last which presupposes all the rest, 
and neither conduces to nor implies any thing to fol- 
low it. 

(3.) Put each intermediate step after that which it 
presupposes, and before all those which depend upon it. 



198 LOGIC. — TAB.T n. [chap. 

(4.) Omit as extraneous matter whatever is not 
conducive to the End in view. 

(5.) If there are intermediate steps requiring to 
occupy the same place, they may be arranged with 
regard to convenience or taste merely. 

765. Method can never be discussed and treated in 
any full and satisfactory way, except in connection 
The discussion wlth a dlscussiou of the Means and the Mat- 
piie^^^i'^'know- ter, or at least by presuming that they are 
Mafer and the already known. To teach the Method of 
Means. ^^j trade or art would be to teach the trade 
or art itself. We could not teach the Method of ship- 
building, for instance, without teaching the whole trade 
of building ships. For the order in which each act 
should come, each material be used, and the way in 
which these details should be disposed of, must depend 
upon the character of the details themselves to such an 
extent as to involve Method and Means most inextri- 
cably in the same discussion. 

766. For this reason it will be necessary to limit 
Means of limit- oursclvcs iu the discussiou to some special 
je?t. ^ ^ ' and definite sphere. This we shall best ac- 
complish by considering those influences which are 
external to Method itself properly considered, but 
which do nevertheless determine it, and constitute 
species and varieties in Method. 

SECTION III. 
Of the Ideas which determine Method. 

767. I have said that Method is the result of mind 
in its application to the attainment of any End. 

768. But there may be several Ways or Methods to 
spverai Me- tlic Same End. If I wish to s:o to the neie^h- 

thods to the t . .n p • i x • i j. 

same End. bonug Village, lor instance, 1 may wish to 
go as quickly as possible ; in that case I should select 
my means and my method or way with reference to 
quickness of time. If the time is no object, the ease 



I.] OF THE ELEMENTS OF METHOD. SECT. m. 199 

with which the journey may be accomplished may 
determine me to select other means and another route. 
Or again, if pleasure be the leading object, I may select 
still different means and still a different route from 
what I should if speed or ease alone were to be con- 
sulted. 

Y69. There are Five Ideas which determine the 
mind in its choice of a Method — two of them Five ideas that 
are relative — Ideas of the Understanding, as thids""'""^ 
the Germans would call them ; and three are abso- 
lute — Ideas of the Keason. The two former are Plea- 
sure and Utility ; the three latter are the Good, the 
Beautiful, and the True.^ 

770. The two former, Pleasure and Utility, I have 
called relative Ideas, because they always Measure, why 
relate to the person by whom the Method is ^■eiative. 
determined. What is pleasant is pleasant not abso- 
lutely and in itself, but only because it is found to 
afford pleasure to him who experiences it ; the same 
thing, as we often see, may be pleasant to one and un- 
pleasant to another. 

771. So of Utility. Nothing is useful in itself or 
absolutely. It is useful only to some end; utility also re- 
and the end by comparison with which we ^^^''^®- 
judge a thing to be useful is also personal and of time. 
If we ask why a thing is useful, we always come round 
at last as the final answer to the fact, that it conduces 
to some worldly object which we wish to have accom- 
plished. 

772. But the Good, the Beautiful, and the True are 
absolute. To say that a thing is Beautiful ^he Good, the 
because it pleases, is merely to give our fhe^ xmi; abTo*? 
means of knowing a thing for the reality of ^'^^^• 

* There may be good reasons for reckoning the Plausible as sustaining 
the same relation to the True that the Pleasant does to the Beautiful, and 
the Useful to the Good. But I have chosen not to do so ; hut rather to 
look upon the Plausible as merely one subordinate species of the Useful ; 
namely, that which is useful for conviction and persuasion, irrespective of 
the truth of that which those whom we address are to be persuaded or 
convinced to do. 



200 LOGIC. — PART II. [chap. 

the thing itself. To say that an act is good because it 
is useful is to change the standard altogether. The 
absurdity of the change is seen, when instead of speak- 
ing of moral excellence or the character of God, we 
say that it is Useful instead of it is Good. 

773. The life of man is for the most part controlled 
and directed by the relative Ideas of Utility and Plea- 
sure. Devotion to the absolute Ideas im- 

The Relative -,, ,-. , r. m> n 1 1* ^ i 

Ideas most pro- plics Something 01 selt-iorgetiuiness and 
orSry ufe of sclf-immolation that rises into heroism and 
°'^°' religion. It implies an elevation and dignity 

of character which is by no means every where to be 
met with. 

774. These several Ideas when developed into prac- 
These Ideas tical prcccpts, givc risc to systems or codes 

rules Sfictiin.^ of actiou. Thus the Idea of Pleasure be- 
comes the Epicurean theory of Ethics. Pleasure is the 
Highest Good, and Virtue is only the wise and pru- 
dent pursuit of Pleasure. The Idea of Utility gives 
rise to the system of expediency, the Happiness of 
Man ; and each one's happiness is for himself the High- 
est Good which he can propose to himself to accom- 
plish. Hence whatever is useful towards the accom- 
plishment of this end is right, and the pursuit of it is 
virtue. 

775. The Idea of the Beautiful is developed into 
Development what has comc to bc called Esthetics ; and 

Ideas. ^^ ^ ® the Idea of the Good determines Ethics, or 
the law of right action. And Logic in its comprehen- 
sive sense is determined by the Idea of Truth. Es- 
thetics says this must be so because it is beautiful. 
Ethics says this must be so because it is right, and 
Lo^c says this must be so because so it is conforiiied 
to Truth, 

776. These Ideas sustain towards each other a sort 
Relation of of svb-contravii opposition, in consequence 

these Ideas to *j x. x. ' -l 

each other. of which ouc may prevail and control the 
Method without influence from the others, and yet no 
Method can be formed in which all of the Ideas can 



I.] OF THE ELEMENTS OF METHOD. SECT. HI. 201 

be combined, each in its perfection. At least, man in 
his present state has never been able thus to combine 
these ideas, and we are satisfied with any object when 
in determining its method that idea has had the ascend- 
ency which in the common estimation ought to have 
the controlling influence in such cases. Thus in an act, 
the moral character of which is strongly marked and 
of an unalterable character, as parental affection, filial 
duty, gratitude to benefactors, fidelity to an engage- 
ment, &c., we are shocked and indignant if considera- 
tions of -Esthetics, or of expediency, are allowed to 
take precedence of that controlling influence which 
Eight and Good ought to have in such cases. In the 
fine arts, on the other hand, the artist entirely fails of 
his object unless he subordinates all other considera- 
tions to that of the Beautiful. The same holds true in 
regard to objects whose final cause is Utility. Any 
attempt or pretence of motives of conscience in matters 
which are indifferent in themselves, as in the cut of a 
coat, the color of a hat, the shape of a house, &c., &c., 
is but ridiculous fanaticism ; just as any attempt at the 
display of ornament in cases where utility alone is 
sought for is an offence against good taste, which im- 
plies either a want of culture or a want of sensibility. 
The man who should attempt the ornaments and plea- 
santries of poetry in a mathematical demonstration, 
would be considered hopelessly bad in respect both to 
taste and good sense. 

777. Still however the Ideas of the Beautiful and 
the Useful are so related, that we seldom TheBeauHfui 
pursue the one without some regard to the f^f ^ow com- 
other. Seldom do we so far abandon our- ^^"^''• 
selves to the luxurious emotions of delight, awakened 
by the Beautiful either in nature or in art, but that 
considerations of economy and utility come in for some 
share in the control of our actions. Nor is it often 
that the iron rule of necessity so far breaks down the 
spirit or paralyzes the wings of the fancy, that we are 
content with fulfilling the conditions and requirements 

9* 



202 LOGIC. PAKT II. [chap. 

of utility alone. The commonest tool of the mechanic, 
the utensils of the housekeeper, and even the imple- 
ments of the boy who cleans the stables, are all fash- 
ioned and finished with some regard to beauty of 
shape — some regard to good looks — some considera- 
tions of taste. 

778. In most of the transactions of life the desire 
The desire of to combiuc as mucli of usefulness and of 

the maximum i . ^ • -i i • 1 i • 1 

of Beauty and bcautv as practicable, is a leadms; and con- 

Utility combin- , n • *^ ^ .> t r. 'U- j it 

ed. trolling motive, in building a dwelling- 

house, or a church, for instance, utiliiy is the first 
object. But we often sacrifice something, and some- 
times much of utility, for the sake of realizing some 
conception of beauty which has entered into our plans. 
And always do we superadd much to what utility 
alone would require, for the sake of making our struc- 
ture pleasing to the taste. The same remark holds 
equally true in regard to articles of dress, of furniture, 
equipage, and whatever circumstances we may choose 
to surround ourselves with. And rarely do we become 
so hurried with business, so engrossed with care, so 
jaded with over exertion, or broken with affliction and 
disappointment, that we become entirely indiflferent to 
the appearance of things about us. 



SECTION IV. 

Of the Matter of Logical Methods. 

779. The second element to be considered as that 
Matter as de- wliich determines Method, is the Matter on 
termmmg e- ^j^^^j^ eftort or labor is to be bestowed. 
This must precede a consideration of the Means, be- 
cause diff*erent matter will require difi*erent means. 
The '' tools" (which are but the Means of the artisan) 
of a shoemaker, a hatter, and a stonemason, for in- 
stance, are as unlike as the material upon which they 
are to work, and the Means themselv^ must be deter- 
mined by the Matter. 



I.] OF THE ELEMENTS OF METHOD. SECT. IV. 203 

780. For this reason we will hereafter confine 
ourselves to the consideration of those Methods which 
concern the discovery, proof, and communi- Limitation of 
cation of knowledge. ^^^ ^^^j^^*- 

781. We have already reviewed the Matter of Logic 
80 far as the investigation of the Formulse can com- 
mand."^ But its relation to Method requires a recon- 
sideration of it from another point of view, and with 
reference to another end to be accomplished. 

782. When a Judgment affirms of its Subject only 
a property which was necessarily implied in the con 
ception of the Subject itself, the Judgment 

is called an Analytical Judgment. But if syntheui^jud^g- 
it adds to or affirms of the Subject a pro- 
perty which was not necessarily implied in the con- 
ception of the Subject, the Judgment is called Synthe- 
tical, Thus, " Every triangle has three sides," is an 
Analytic Judgment, we cannot conceive of a triangle 
without three sides. Nor can we form a conception 
of a triangle at all without thinking of its three-sided- 
ness. Hence Analytical Judgments, while Analytical 
they serve to amplify our knowledge and put nof^^'ISSease 
our conceptions into Judgments for deduc- knowledge. 
tive purposes, do not increase our knowledge at all. 
But the Proposition, " The angles of a triangle are 
equal to two right angles," is a Synthetic Judgment. 
For although this is a necessary truth, yet the property 
affirmed in the Predicate is not a part of the matter of 
the conception of a triangle, as is obvious from the 
fact that we may know what a triangle is without 
knowing this property of triangles. Hence a Synthetic 
Judgment always adds to the stock of our knowledge. 

783. An Analytic Judgment affirms of a Subject 
only what was necessarily implied in the conception 
of the Subject. But it is one thing to be Matter of the 
implied in the conception of a Subject, and SiXfiTthe 
another to be implied in the existence or f^l^^^ °^ ^^" 

* Ctap. I. of Part. L 



204 LOGIC. PART II. [chap. 

reality of the Subject; thus, to take the example just 
given, " three-sidedness,^^ is necessarily implied in the 
conception of a triangle. But " the equality of its 
angles to two right angles^'^ though necessarily implied 
in the nature and reality of the triangle, is not, as we 
have seen, necessarily implied in the conception of it. 
A triangle however could no more be a reality, that is 
a triangle, without the equality of its angles to two 
right angles, than without its three-sidedness. 

784. Now the Matter of all Judgments, whether 
Synthetic or Analytic, which aflGirm of any Subject 

Necessary ^"^1 w^hat is ucccssary to its reality as an 
Matter. individual in any particular genus, is called 

Necessary Matter. Or in other words, all Judgments 
based upon the principle of contradiction are in Neces- 

Effect of con- '^<^^2/ Matter. Hence, if we deny the Predi- 
tradiction. ^^^^ ^^ ncccssarily exclude the Subject, not 
from reality, but from the genus which the Subject 
denotes. Thus if I predicate of a circle that its radii 
are not all equal to each other, it may be a figure and 
a curve, but it is not a circle."^ 

* There is no simple term that may not be affirmed as a Predicate of 
something either real, possible, or impossible in the abstract ; though not 
always in the concrete (Part. I. 279, 280). Thus we may not always be able 
to predicate " walking^'' in the concrete of any individual, but in the abstract 
we may always predicate it not only of man but also of other beings, as a 
property which we conceive as belonging to them in posse if not in esse — iu 
4i^Te\€X€La if not eV iuepyeia. Hence when the Predicate is a simple term, 
the Principle of contradiction can only exclude the subject spoken of from 
the genus denoted by the name given to it, and used as a subject in the 
Proposition. As when we say, " this circle has unequal radii," the Prin- 
ciple of contradiction, if apphed, would exclude the figure spoken of from 
the genus " circle," though it might leave it in some other genus of reali- 
ties — as the ellipse for instance. 

But we sometimes have a complex Predicate, which, by the Principle of 
contradiction, would exclude the Subject not only from reality but from 
possibility also. Thus if one should say, " this figure is a two-sided tri- 
angle," — *' two-sidedness" and "triangularity" cannot be combined as 
predicates of the same subject. Hence their combination produces a com- 
plex term, which can be affirmed of nothing, whether real or possible, and 
the Proposition affirms no judgment. It is mere non-sense. It wiU be 
found that the number of such that one meets with in his intercourse with 
human minds, whether orally or in books, is vastly greater than he would 
at first expect. 



I.] OF THE ELEMENTS OF METHOD. — SECT. lY. 205 

785. It is manifest, however, that Judgments in 
Necessary Matter may affirm of a Subject something 
more than the Essentia of its conception, judgments in 
Most of the properties of the figures with S' m'ay^ffirm 
which Geometry is concerned, are proper- fhSffhi^l^en^. 
ties conjoined in some such way with the ^•^• 
Essentia of their several genera, and yet they are not 
Essentia, for they are not known as soon as the con- 
ception of the class is formed. One knows what a circle 
or an ellipse is, for instance (so^that he could never be 
mistaken in deciding with reg'ard to any figure, whe- 
ther it is a circle, or an ellipse, or not), long before he 
knows all the properties which are implied in the very 
nature of those curves. 

786. But if we pass from the consideration of such 
matter to the consideration of the realities ^^.^^^^ 
of beins:, we find there that any obiect of have properties 

,T 1,1 i» !•! J 1 not contained 

thought has properties which not only are in this, ciass- 
not contained in its class-conception (as the ^^"^^^ ^^"' 
Essentia of the proximate genus has with propriety 
been called), but which do not appear to us to be in 
any way necessarily connected with the matter of that 
conception. Such in fact are most of the properties 
of the objects of the natural world ; they con- contingent 
stitute what is called Contingent Matter — for ^^"^^• 
it seems to be contingent or dependent upon the will 
of the Creator, whether they should have such proper- 
ties or not."^ 

* Necessary Matter is that which is affirmed or denied on the Principle 
of Identity or Contradiction. 

But there is a class of philosophers who either ignore or deny the dif- 
ference hetween Necessary and Contingent Matter. Among those is Mill 
in his Logic, Prof. Whewell has affirmed the distinction on two grounds : 

(1.) That Necessary Judgments affirm what has never been a matter 
of experience, as when we say, " Two straight lines can never inclose a 
space." 

To this Mr. Mill replies, that what we can construct in ike imaginaticm 
is as much a matter of experience as that which we may have seen in the 
reality of being. We can imagine two straight lines infinitely extended, 
and yet not inclosing a space. 

(2.) Prof. Whewell said also that the Judgments which we call Neces- 



206 LOGIC. — PART n. [ghap 

787. Now all Judgments, whether analytical or 
Judgments in svnthetic, in Necessary Matter are called 

Necessary Mat- tj i ••^l.^'TJ ^ 

x^xa'priori. Judgments a jpr%OT% '^ that is. Judgments 
which are affirmed from a consideration of what was 
contained or necessarily implied in the very conception 
Judgments in ^^ ^hc objcct. But all Judguieuts in Con- 
contingentMat- tingcut Matter are called Judgments a pos- 
^^'^' teviori ; that is. Judgments which are and 

can be known to be true only posterior to and after an 
acquaintance with the Subject as existing among the 
realities of being. 

788. Necessary Matter, therefore, consists of the 
conceptions of realities of truth ; and Contingent Mat- 

Necessaryand ^cr, iu what is added thereto to constitute 
t^e?"ii"thf s^me them rcalitics of being. Thus, suppose I 
conception. form a conception of a point in space — as a 
point it has no extension. It is a reality of truth but 
not of being. I conceive that point to move directly 
towards another point in space — the path which the 
point is thus conceived to describe, I call a straight 

sary, differ from the Contingent in that we cannot even imagine or con- 
ceive of an exception to the Necessary, whereas all Contingent Propositions 
actually have exceptions. 

But Mr. Mill replies, that tjiis rather proves the limited capacity of our 
powers than any thing else. Many things have now become true which 
not long ago were not and could not have been conceived as true or pos- 
sible. 

Without deciding upon the merits of this controversy thus waged, I wiU 
add for the consideration of those who think with Mr. Mill, that all men 
perceive a difference in the kind of certainty which they feel in the truth, 
that " every triangle has three sides ; " and those Contingent Propositions 
which we are continually offering. Thus I say, " The rose is red — the 
apple is unripe — the horse is gray — that man has ten fingers," — every body 
sees that the one may have ten fingers and yet be a man, that a horse may 
cease to be gray without ceasing to be a horse, that an apple may be un- 
ripe, or a rose yeUow. But if the (so called) triangle has not three sides, 
it is Twwcalled, it is no triangle, and the Proposition cannot be true. Change 
the quahty of the Copula and you destroy the Logical Essentia of the Sub- 
ject. But in the other examples given, this change in the quality of the 
Copula may be made without changing the Essentia of the Subject at all, 
and thus causing it to cease to be of the species to which b^^ its name we 
had referred it. No one, I suppose, will deny the diflereuce thus pointed 
out between those two classes of Judgments — we make it a Differentia of 
the Species, the one Necessary and the other Contingent Judgment3. 



om 



I.] OF THE ELEMENTS OF METHOD. SECT. IV. 207 

line — the line also is only a reality of truth. I suppose 
the point to move again towards another point not in 
that straight line. It generates another straight line. 
I conceive it to move again directly to the point from 
which it started. It has now generated a third line in 
such a relation to the other two as that it joins them, and 
they then make a triangle. The triangle is a reality of 
truth ; and I conceive of it, that is, have a conception 
of it, as a ligure with three straight sides, including 
three angles. These two properties are the matter of 
my class-conception. From this I deduce ^ j^^i^n de 
a priori the further property, that the sum fhe^TiLs^oS 
of its angles are just half as much as the ^^p^ion. 
sum of all the angles that can be formed around any one 
point in space ; and that if I know the size of any one 
of its angles and the two adjacent sides, or if I know 
the length of one side and the size of the two adjacent 
angles, I can determine the size of the other angles 
and the length of the other sides. In the same way, I 
may construct in my mind a rectangle, a circle, an 
ellipse, &c., and of each I can ascertain a priori^ many 
properties which did not enter into the class-conception 
of those figures. 

789. But if I take up my crayon, before a black- 
board, and make a dot, calling that a point, 
and make a mark as straight as I can, call- tion IrawnS 
ing that a line, &c., these figures on the ^^^^'^°^" 
board are not the realities of being of which I had 
formed the conception, and of which I had demon- 
strated, or of which I could demonstrate those propo- 
sitions. These marks may represent^ but they are not 
the point, the line, the triangle, &c. I can 
predicate much of those marks that could predtclteJ" of 
not be predicated of the realities of being thanofSlecoIJ^ 
which they represent. Thus the mark has ''^^^^""' 
breadth, the line none — the mark has color, and is 
upon a ground of a different color — a white mark on a 
blackboard, for instance ; the line has no such pro- 
perties. These realities of truth, the point, the line, &c.j 



208 LOGIC. — FAUT n. [chap. 

have been done or made into facts — realities of being in 
the outer world. They have been clothed upon with 
visible forms, having properties of their own in addition 
to those contained in their class-conception. Now all 
these properties are Contin2:ent Matter. It 

The difference ^ ^ ■■- 'ii i ^i t mi 

in Contingent acpends upou my Will whether 1 will give 
to my conception of a triangle an outward 
expression on the blackboard or not ; and whether that 
expression shall be with a white mark or a mark of 
another color ; whether the mark shall be small and 
smooth, or broad, rough, and irregular, &c. 

Y90. Let us pass to another class of objects. Sup- 
creation. posc thc Diviuc Mind to have constructed a 
conception or an idea of the various classes of beings 
included in the Creation. As existent substantial reali 
ties each individual must consist of Matter, extended 
so as to fill limits in space and to be impenetrable ; 
be composed of particles, every one of which should 
have an attraction for every other particle, and this sub- 
stantial matter must be without life or capacity of 
originating motion or of acting, except as it was acted 
upon by a spirit either within or from without each 
i^ lividual object. 

791. Now, here we have the class-conception of the 
objects which have a material existence. From this we 

A priori mfer- ^^u dcducc a prioH many of the funda- 
cSnclpHoS" ^Sf inental principles of the Natural Sciences. 
Matter. From extciision must follow the divisibility 

of all material objects ; from attraction must follow 
density and the phenomena of gravitation ; from in- 
ertia the three laws of motion may be deduced, and 
so on. We should, however, know nothing of the 
phenomena of light, of color, of electricity, of sound, 
of chemical combination, &c., from these mere class- 
conceptions. 

792. But let this Divine Conception pass into 
Contingent reality of existence — be done into a fact, 

B-aniy^ imTifed aud cacli plccc of matter necessarily takes 
if be^Sg/^^^^ upon itself, or rather its Creator puts upon 



I.] OF THE ELEMENTS OF METHOD. — SECT. IV. 209 

it properties and relations not implied in the class- 
conception or resulting therefrom ; but which are, 
however, necessary to the reality of each individual 
object among the facts of existence. The specific color 
and shape of each piece of matter, for instance, though 
it must have some color and shape, were to be deter- 
mined by the will of the Creator, and not necessarily 
implied in the conception or the resolution to give it 
reality of being. Those properties of the outward form 
of the conception — its material body — are contingent Mat- 
like the diagrams by which we represent ter how known, 
our conceptions of a triangle, a pyramid, &c., matters 
of choice and chosen by ourselves, and can never be 
known by any other mind until he has learned them 
either by revelation — that is, verbal communication 
from ourselves, or by an inspection and study of the 
diagram which we have drawn. 

793. From the foregoing considerations of the Mat- 
ter of Judgments, we may divide the Pro- a new ciassifi- 
perties of Objects again with reference to peAtes.** 
Method on another principle and into other classes. 

794. Thus all of those Properties which are in- 
cluded in the class-conception maybe called Material pro- 
Material Properties ; as three-angledness and p^'^^^^- 
three-sidedness of a triangle, extension and inertia in 
matter, &c. Then all of those Properties which are 
necessarily implied in, and deducible 'a priori from 
these Material Properties may be called the Implied 
Properties, as the equality of the angles of a implied pro- 
triangle to two right angles, divisibility from p^'^^^''- 

the extension of matter, and the laws of motion from 
its inertia. 

795. Those properties of bodies which serve to 
make the species of objects in the reality of properties of 
being, such as two-footedness of man, canine b^fng'^may be 
teeth or the carnivora, weh-footedness of "^^teriai. 
aquatic birds, unsupportedness of falling bodies, &c., 
may indeed be assumed as Material Properties in our 
conception of the class, and as such we may reason 



210 LOGIC. — ^PAKT n. [chap. 

from them a priori to other implied properties, just 
as from the three-angledness of a triangle in Mathe- 
matics. 

796. But for the most part, and always for all the 
purposes of science, these properties are learned apos- 

. . teriori^ from actual observation of the indi- 
dicaSvl^ ' oV"a viduals cxistiug in the reality of being. 
Each of these properties, however, is con- 
nected with and is suggestive of a Final Cause, for 
which it was bestowed upon individuals of that class ; 
the two-footedness of man was designed as a means to 
the upright position in which he walks ; and so through- 
out the material world we connect those properties 
which are differentia of species with something in the 
habits or modes of the individuals of the species, as 
two-footedness with erectness of stature — canine teeth 
with carnivorousness, &c. 

797. Now in reference to this fact we may call the 
Call Formal formcr Propcrtics which are indicative of 

Properties. ^^ Final Causc the Formal Properties ; 
and those which are thus connected with them and 

Modal Pro- ii^plied in their reality, we may call the 
perties. Modal Propcrtics. And all those Proper- 

ties which are susceptible of more and less, as size^ 

Variable Pro- temperature^ density^ mighty &c., we may 
perties. q^^"^ variobU Properties. 

798. It will be observed that Material and Formal 
Material and are uot coordluate terms, but only terms 

orSteTeriSt dcuotiug alternate conceptions. Material 
and Implied are the coordinates in a priori Matter. 
Formal and Modal are the coordinates in a posteriori 
Accidental and Matter. Thcu bcsidcs these w^e have the 
pe'^tfi^ma/'be- Accidcutal aud Variable Properties. These, 
Slriai ^'^^oJ however, may become either Material or 
Formal. Formal. But when they do become so they 

cease so far forth as they are Material or Formal to be 
accidental to the individuals into whose class-concep- 
tion they have thus entered. Thus, the " unsupport- 
edness'^ of bodies which fall is but an accidental 



I.] OF THE ELEMENTS OF METHOD. SECT. IV. 211 

property of those bodies as masses of matter. But 
we assume it as a Formal Property with reference to 
the Modal Property denoted by the word ^^ falling ; " 
when we say that " all bodies which are unsupported, 
fall to the ground." So too " right-angledness " is but 
accidental to " triangle ; " but when we take it into 
our class-conception we have " right-angled triangles," 
and then it becomes Material. 

799. Now as the Matter of all a priori Judgments 
is necessary Matter, if the Judp-ment be af- 

n A- ', I ^ J • i • 'fhe Contra- 

Urmative, its contrary or contradictory is dictoryofjudg- 

TTT ■' 7 -,.. Ti* j' 1 ments in Neces- 

called an absurdity, it is not merely an sary Matter ab- 
error. Of this kind are all mathematical 
and all analytic Judgments. If the Judgments be 
negative, the aflSrmative would give a nihU purum — 
that is, an impossibility ; as that two and two make 
five, two straight lines may inclose a space, an effect 
without a cause. 

800. In Necessary Matter if the subaltern is true, 
its universal must be true also. That is, 

K-r . . * J 1 J 1 Immediate In- 

1 IS true A must be true also. ferences from 

If O is true E must be true also. Necl?sl?y^Mat" 

And all contraries are virtually contradic- 
tories, and only one of the sub-contraries I and O can 
be true. 

801. Contingent Matter is also divided into Natural 
and Moral. 

Although the order of Nature seems to be per- 
fectly stable and uniform, we conceive this order as 
having been established by an Intelligent Knowledge 
Author as the choice of His will. In many Siatter^"«°!f^- 
respects w^e can conceive of it being differ- ^^''''^^^''^ 
ent from what it is, and for the most part we know 
nothing of its facts, principles, or laws until we have 
observed and studied them from actual facts and oc- 
currences. Hence clearly the knowledge of Nature is 
a posteriori^ and the Matter itself is contingent. 

802. But so great is the uniformity and constancy 
of its operations and processes, that we consider its 



212 LOGIC. — PART n. [chap. 

laws as almost as certain as the deductions of mathe- 
physicai cer Hiatics themselves. But the certainty is not 
tainty. quitc SO great (since there always may be 

exceptions), and it is different in kind. Hence we call 
it a physical certainty. And the contradictory of any 
proposition enunciating a physical truth or certainty 
would not be an absurdity, but simply a falsehood or 
error. 

803. But in the actions of man there is no such 
uniformity as we find in ISTature. His moral freedom 
Moral Matter, placcs liis acts at the disposal of his will, 
rather than of any law which operates uniformly in all 
similar cases. 

804. Hence in the actions of man there is not a 
necessity of any kind, in the proper sense of the word. 
Since, however, the will of man is influenced in some 
measure by motives external to itself, any strong com- 
MoraiandPhy- biuatiou of motivcs wiU usually induce a 
sicai Necessity, particular kind of action ; and hence this 
class of actions are said to constitute a sort of moral 
necessity. The objects in Nature are not conceived as 
having any liberty to choose what they will do, or any 
power to act except as they are acted upon. — Hence 
the physical necessity. On the other hand, man is 
conceived as having the power to choose what he will 
do, to act in accordance with external forces or against 
them ; and hence his acts are not under the same law 
as that which determines the motions, the facts, and 
events in Nature. 

805. Still, however, there is some uniformity in the 
acts of men under similar circumstances ; and hence a 
knowledge of the circumstances always gives a strong 

Moral Certain- pTobobiUty as to tlic coursc ouc wiU pursuc. 
*^- This, when it exists in but a low degree, 

is called, merely probability. But when the proba- 
bility becomes very great, it is called a Tnoral cer- 
tainty. 

806. The same principles are also extended to the 
events of Providence ; that is, future events whicli are 



I.] OF THE ELEMENTS OF METHOD. — SECT. IV. 213 

not, SO far as we know, under the control of any phy- 
sical laws and causes, but which are sup- Moral cer- 
posed to depend upon the overruling Provi- Jhl^a^cts^'of pro" 
dence of God. What the probability lacks ^^^ence. 
of certainty in the two cases, however, depends upon 
two entirely different grounds. In the case of man it 
depends upon the fact that he does not always act 
consistently with himself, or as he ought. But in the 
case of the acts which are conceived as depending upon 
the will of God, the uncertainty in our minds arises 
solely from our not understanding His ways, and the 
laws and principles upon which He acts in His govern- 
ment of the world. 

807. There are some cases, however, in which even 
man may acquire such a character, as that circumstances 
we feel a certainty as great, though different fSSf opMoral 
in kind, as though it were absolute with Certainty. 
regard to the course he will pursue. We know that 
Washington will be patriotic, 'Nej will be brave, 
Howard benevolent, and that St. Paul will hesitate in 
view of no peril to himself in doing what he regards 
as the will of God. 

808. So too in forecasting the conduct of masses 
of men, we can calculate with almost a phy- certainty in 
sical certainty — almost as surely as the mo- Suct^'' ^ol 
tions of the heavenly bodies. Masses can masses of men. 
never differ from one another so much as one indi- 
vidual may differ from another. Nay, when masses 
become quite large, the Political Economist and the 
Statesman can, from knowledge of the circumstances, 
determine beforehand in general terms what course 
men will pursue, and what result they will arrive at, 
almost as certainly as the astronomer can determine 
the return of a comet. 

809. The Matter which thus determines Logical 
Methods admits of being resolved into several ele- 
ments, to which we will refer for a moment, in order 
to get a little more distinct conception of them. 

810. Every object of thought, regarded merely as 



214 Loaio. — ^PABT n. [chap. 

an object about which our thoughts are occupied, 
and over the existence of which in the past and in the 
Facts. present we have no control, may be regarded 

as a FACT. Thus, what one has been, said, or done, 
and even the intention of that which was intended but 
left undone ; whatever exists or has existed, whether 
in the mind alone or embodied in some external form, 
is ^fact. 

811. The word ^^facV^ is ixovn facio^ to do, and is 
used with reference to something done^ or something 
which has been brought into the reality of exist- 
ence. 

812. We distinguish a fact from an event by applj^- 
Event. ing the word ''-fact " to that which remains 
as the result of the making. But by an " event^'' on 
the other hand, we mean the happening or occurring 
itself, even if it leaves no fact, or factum^ thing done, 
behind. But an " event " is the mere happening, it is 
a mere phenomenon ; it appears in time, is instanta- 
Events pass in- h^ous, and thcu ccascs. Hence the same 
to Facts. thing may be regarded as both a fact and 
an event ; the birth of Napoleon, for instance, was 
both an event and a fact. As an event, it happened 
or occurred on a certain day, at a certain hour and 
moment — was real as an event then and then only. 
But as a fact, a thing done — a thing that is remem- 
bered, enters into and forms a part of history, it is as 
real now as it ever was, and must remain so forever. 

813. Again, we distinguish " facts " from mere 
Facts distin- rcalities of truth. A point, a line, a triangle, 

conclptions'^'" would hardly be called facts ; they are rather 
realities of truth than of being, of which the mind forms 
conceptions by means of its own activity. The dot, 
the mark, &c., are not points and lines, they only re- 
present them. 

814. We also distinguish ^^ facts " from Ideas. We 
Facts distin- could hardly speak of time, of space, of 

fdeas^ ^"°° cause, of substance, of truth, as facts. AVe 
do not conceive of them as made, but rather as neces- 



I.] OF THE ELEMENTS OF METHOD. SECT. IV. 215 

sary and eternal realities anterior to any act of creation, 
any act of making or conceiving them. 

815. We distinguish " facts " from " fancies " or 
" phantasms " also. The facts are supposed 

to have an obiective reality of beinp*. The guish^ed from 

T . i? 1 Ti. • Fancies. 

phantasm or fancy has none. It is a mere 
combination of properties in the mind, to form that 
which is the representation of nothing that exists or is 
supposed to exist. 

816. Any facts which attend upon or surround 
another fact as their principal are called circumstances. 
circumstances, 

817. Facts, as they first become objects of thought, 
are complex wholes. We do not perceive Facts at first 
color, size, shape, density, &c., each sepa- complex, 
rately and ojie after the other ; and then combine them 
by any conscious or voluntary operation into the per- 
ception of an object. But we perceive the object as 
a whole, and then by an act of reflection w^ consider 
these properties separately. 

818. The process by which we resolve the per- 
ceived whole into its parts is called Analy- Analysis. 
SIS ; and the act of considering one of the parts alone, 
and by itself is called Abstraction / and the Abstraction. 
name by which the part is thus designated is called an 
abstract term. 

819. Analysis has different methods in different 
kinds of matter ; thus the chemist has one Different kinds 
kind of Analysis, the mathematician another, of Analysis, 
and the metaphysician another..^ 

* "St. John Damascene says there are three kinds of Analysis ; the 
first resolves compounds into their simple elements ; the second resolves the 
syllogism into its several parts ; and the third or mathematical, consists in 
admitting the correctness of a certain principle in order to arrive at the 
knowledge of an important truth." — Blakey's Hist, of Int. Philosophy^ vol. I. 
p. 274. 

Pappus, a mathematician of Alexandria, A. D. 400, and author of 
" Mathematical Collections," says in the preface to his seventh book : — 
" Analysis is the course which setting out from the thing sought, and which 
for the moment is taken for granted, conducts by a series of consequences 



216 LOGIC. — PAKT u. [chap. 

820. Logical Analysis, of which alone we are now 
Logical Analysis. Speaking, consists in resolving the concep- 
tion of any object of thought into those elementary 
parts which go to make up the adequate conception 
of that object. The Analysis is called proximate when 
Proximate An- ^hc parts, any or all of them, admit of further 
aiysis & Parts, aualysls. Thus the Analysis of the concep- 
tion of any object into substance, attributes, and modes 
is proximate. For the attributes and modes admit of 
further analysis. But when the Analysis can go no 
further, because there is no part that admits of further 

Last or uiti- aualysls, it is called the last analysis, and 
mate Analysis. j^]^q parts givcu out by it are called ultimate 
parts. Thus, I analyze my conception of a piece of 
gold before me into the substance, which I will call 
gold ; the j^ropertieSj which I will call extension, yel- 
low, ductile, &c. ; and into the modes, as polished, coin, 
orname7it, utensil, &c., &c. 

821. By a process which is the reverse of Analysis, 
Synthesis. callcd SYNTHESIS, wc put togcthcr thcsc ulti- 
mate elements to construct the complex whole. Thus, 
as by analysis the chemist reduces water to oxygen 
and hydrogen, so by synthesis he puts these elements 
together and combines them into water again. 

822. So also in Logical Synthesis we put together 
in the unity of consciousness the elements of which a 

Synthesis of conccptlon is composcd, and form the con- 
conceptions. ccptiou. It is by this process of analysis 
and synthesis that a conception passes from one mind 
to another. Again, with the substance for subject and 
any one of the properties or modes for a predicate, we 

to something already known, or placed among the number of principles ad- 
mitted to be true. By this method, therefore, we ascend from a truth or 
a proposition to its antecedents ; and we call it Analysis or resolution, as if 
indicating an inverted solution. In Synthesis^ on the contrary, we set out 
from the proposition, which is the last in the Analysis." In the method of 
Analysis, " If the result is true the proposition which we assumed at the 
outset is true also, and the direct demonstration is obtained [synthetically] 
by stating in an inverse order the different parts of the Analysis. If the 
ultimate consequence is false the proposition was false also." 



I.] OF THE ELEMENTS OF METHOD. SECT. IV. 217 

unite them into a judgment ; these judgments we com- 
bine into a syllogism, &c. And a set of judgments 
combined into a whole by means of the unity of their 
several subjects is called a " System,'^^ The system. 

word is from a root of similar import as " synthesis^ 

823. Now when the evidence or grounds upon 
which any system is based is such as to leave no doubt 
of its truth, as in mathematics, we call it a truth or the 
truth. But if its truth be still doubtful, and Truth, 
received by those who accept it, on grounds which are 
not satisfactory, or not generally acknowledged as such, 
we call it an Opinion, Truth is supposed to opinion, 
rest upon grounds which are entirely independent of 
choice, passion, prejudice, or any wishes or feelings of 
a personal character. Opinion, on the other hand, is 
always supposed to be indebted for its reception in 
some measure to the good will or wishes of those 
who hold it ; that is, they hold it from choice in part 
at least, and not altogether from the unbiassed convic- 
tions of their own judgments, or the necessary laws of 
belief. 

824. When any system of judgments, or a judg- 
ment singly is regarded as explaining a fact or a series 
of them, it is called a Theory. Thus we have Theory, 
the facts of bodies falling to the earth ; and we have 
the theory of gravity — namely, that the Earth attracts 
them. But the agency or efficacy here attributed to 
the Earth is a mere theory. It may be consistent with 
the facts. But it is after all a theory, and a theory 
only. We have theories of light, theories of electri- 
city, &c. ; that is, some explanation of the facts, which 
goes beyond the facts themselves, and serves to give 
them a scientific unity and completeness ; and it is 
sometimes the case that the facts renaaining precisely 
the same, two or more theories will each of 

them explain the facts so far as they are at ries^^'^for fhe 
present known as well as the other. This I ^^°^® ^''^'' 
believe to be the case with regard to the two theories 
of light — the emanation and the undulation theories : 

10 



218 LOGIC. — PAET n. [chap* 

and tlie two theories of electricity — the theory of a sin- 
gle fluid and the theory of two fluids. 

825. When before we have facts enough to form a 
theory, we guess at what the true theory or explana- 
conjecture. tlou of the facts wiU bc — this guess is called 
a Conjecture. 

826. From the foregoing definition it is evident 
Analysis pre- that thc coUcction aud analysis of the facts 

cedes Synthe- , t t • jI*' t r» 

sis. must always precede m the order oi a cor- 

rect method, the synthesis or putting them together 
into a system, or combining them for the construction 
of a theory or an argument. 

827. But as the accumulation and careful analysis 
of facts is slow, men often desire to construct a 
theory or system before this preparatory work has 
Hypothesis. becu douc. In this case they are often com- 
pelled to guess at what the fact would be if it were 
known. Such a guess is called a Hypothesis^ or some- 
thing placed under to support our theory or system. 

Our subject will henceforth divide itself into the 

Division of the ^ur chicf parts — (1) Methods of Investiga- 

subject. ^^^^ . (2) Methods of Proof; (3) Methods of 

Disproof or Refutation ; and (4) Methods of Instruction. 

828. These subdivisions of the present part of our 
These Parts ra- Trcatisc arc rather alternate than coordinate 
than colx&t parts. Thcro is no investigation that does 

not carry with it some conviction of the cer- 
tainty of its result ; that is, some kind and amount of 
proof. So, too, there is no method of proof that is not 
m some measure an investigation into the truth of what 
it undertakes to prove. Disproof is of course a method 
of proof And Instruction, or the construction of the 
things known into systems and sciences, implies some- 
thing of investigation and proof. 

Still, however, a division seems to be desirable ; 
and I shall refer the various methods and topics to one 
Principle of c>r auothcr of the four class terms, accord- 
ciossification. jj^g ^g ^^^ which I havc announced as the 
leading subject in each, is or is not the prominent trait 
in the Method to be discussed. 



n.J METHODS OF INVESTIGATION. — ^SECT. I. 219 



CHAPTEE n. 

METHODS OF INVESTIGATION. 



SECTION I. 

Of Investigation. 

829. I remarked in Part I. [451], that where the 
Question is concerning the Copula, it is to be answered 
by some one of the Formulae. The Formula, however, 
presupposes all the Terms as given. In the case of 
Immediate Inference, as well as in all Intuitive Judg- 
ments, there is no Term needed except those which 
appear in the Judgment or Conclusion itself. Necessity for 
But we may often have a Judgment to be finding Terms. 
proved, with no Exposita from which it can be deduced 
by Immediate Inference, and no Middle Term given 
by means of which it can be proved as a Deductive 
Judgment. Hence we may have occasion to find a 
Middle Term. And in all cases where the Question 
is concerning the Major Term that Term is still to be 
found. 

830. The finding of these Terms is what we call 
Investigation,^ Whether the Term to be sought be to 

* The subject wliich we treat in tliis Chapter is to a considerable ex- 
tent the same as that which Aristotle and the ancients generally treated 
under the head of " Jbp«<^s" or "Z^;" for the reason, as Mansel ob- 
serves, that '* it is the 'place in which we look for Middle Terms." Instead 
of the place where we may find them, I have made it a Treatise on the Methods 
ofjmding them. 

Of these loci the Schoolmen made two classes : " Maximce "—that is, 



220 LOGIC. — PART n. [chap, 

be used as Middle Term or not, it must be found as a 
. Investigation Predicate to tho subject ofour inquirj. In the 
pred?ca?es "^ ° Mcthods of Investigation, therefore, we are 
seeking some term which we may predicate of a given 
subject ; and if we wish to use it as a Middle Term to 
establish a Copula, it must be such an one as can be 
used as subject to that Term which we wish to afl&rm 
as Predicate of it as Major Term. Thus, if we wish to 
prove that S is P, we must find a Term as M, which 
we can predicate of S (S is M), and of which we can 
predicate P, as M is P, and we then can affirm our 
conclusion S is P in the First Figure. 

831. The point then in which all the Methods of 
Point common luvcstigatiou uuitc is this : that they are 

of investilation! Mcthods of finding what may be predicated 
of any given subject. 

832. Methods of Investigation, therefore, always 
presuppose the subject to be given ; that is, we must 

Subjects given havc somcthiue^ to investi^cate ; and we may 

by the sphere -i 'i • i^ *i. i. i t_ j.i 

only. nave it given by its sphere only, or by the 

matter of its class-conception determining its sphere. 
Thus I may remember that something occurred with- 
out remembering what it was [52, 53]. I may know 
that there is something in a given room or place with- 
out knowing what it is ; that is, I have the sphere of 
the conception only. 

833. In this case the first thing is to learn what the 
subject is. This we do by acquiring the matter of its 
The first thing class-conccptlon. I may test it by my own 

ihe '^lis^con^ senses — see it, touch it, taste it, smell it, 
ception. handle it, &c., in which case I form the con- 

ception directly from the object itself This Method is 
By Observation, callcd OhseTvatiou, Or I may ask some one 

Maxims ; DifferentioB Mcuximarum^^ The former, as the word denotes, were 
Maxims ; that is, the highest generahzation of truth (Maxima Genera) — 
to be used as Major Premises in Processes of Deductions. As such, they 
of course contained the Middle Term, and furnished thus the means of 
proving the Copula of the desired Conclusion. The Differentue Maximarum 
consisted of one or more words expressive of the point in which one Maxim 
differed from another. 



II.] METHODS OF mVESTIGATION. SECT. I. 221 

else what the subject is, and receive from him either its 
name or a description of it. In either case I form the 
conception from the observation of others — that is, from 
their Testimony ; in which they communicate By Testimony. 
to me what they have observed. This is the Method of 
Testimony ; and the only difference between an an- 
swer giving a name to the subject and a description is, 
that the former implies what is expressly stated in the 
latter. 

834 At the first observation we cannot determine 
whether the observed property be any thing Distinction of 
more than a separable accident or not. On Tt^'^e'^le'Sond 
a second observation of the same individual, observation. 
we decide at once that all of the properties that were 
different in the two observations were but separable 
accidents of that individual. And a third and fourth, 
as well as each successive observation may, and most 
likely will add to this list of separable accidents some 
properties that had not been so regarded before. 

835. But as soon as our observation has extended 
to two objects, these objects are referred to And a ciassifi- 
a class. The properties which they have in ^^*^°" ^^^°- 
common are for the present assumed as Formal, consti- 
tutive of the class ; and those in which they are un- 
like, after deducting what we have seen to be separable 
accidents in each, are regarded as peculiarities or indi- 
vidual properties of each. 

836. A wider observation embracing more indi- 
viduals always brings anew classification, a wider obser- 
Perhaps the bringing in of a third object new'^^cSSmca^ 
may give us two classes— one including two ^'^"• 

of the three objects, while the other will be so unlike 
them as to be regarded as not of the same class with 
the other two. And any change in our classification 
changes our view of the properties ; that which we con- 
sidered an individual peculiarity in one classification, 
becomes a Formal property in another and Material in 
still another. 

837. In the process of classification we soon come 



222 LOGIC. — ^PART n. [chap. 

to find that one property whicli we had made Formal of 
Recognition of oHe class, is alwavs connected with another, 

some properties i»ir» ,^ n i tjt 

as Formal. wnicn 01 coursc tnereiore may be predicated 
of all the individuals in that class as a mode of their 
existence. We see, for instance, that all animals that 
have sharp claws are predacious. "Sharp claws" is 
a Formal property, and " predacious " is a Modal, 
indicating their mode or manner of life. " Unsup- 
ported bodies fall to the ground ; " — " unsupported- 
ness " is the Formal property — " falling to the ground" 
is the Modal property, indicating something concerning 
their mode or condition of being, while objects belong- 
ing to the class of " unsupported bodies." 

838. But " unsupportedness " itself may be and in 
Accidental pro- fact Is oulv au accidcutal property. The 

perties may be t. • ^. -u cc j. J ?) j. 

Formal. samc objcct may be "supported'^ at one 

time and " unsupported " at another, and vice versa. 
Hence the Modal property " falling," will be acci- 
dental also. 

839. But we soon find that some of the properties 
Recognition of which arc not in the class-conception, and 

properties asp I^ f* i ^ j_ . 

implied. 01 course thereiore were not known to us at 

our first acquaintance with the object, are not only 
inseparable from the object so far as we have seen or 
known, but that they are inseparable from it abso- 
lutely. They are Implied properties necessarily result- 
ing from the • combination of the properties which are 
included in the class-conception, as the laws of motion, 
for instance, in the conception of Matter as inert [791]. 

840. This distinction, however, between the Modal 
Distinctiori be- and thc Implied properties cannot be shown 

Fomiai'^propet- a vosteriori. or by any of the Methods of 

ties not shown x j_' l* 

a 'posteriori. Investigation. 

841. Methods of Observation are therefore, and of 
Investigation of ncccssity a posteriori^ with regard to all the 
imphld^roper- Accidcutal aud Modal properties of ob- 

ties a posteri- . , ■*• -^ 

ori. jects. 

842. But in the case of the Implied properties, it is 
for the most part in actual experience no less so. 



n.] METHODS OF INVESTIGATION. SECT. H. 223 

These properties are not included obviously implied pro- 

,T h r" i.' J? -T'lii perties also in- 

m the nrst perception oi an indiviaual ob- vestigated a 
ject. But we first observe the property, ^°^^^^*^^- 
or something which suggests it, and then we prove 
its reality a priori. Thus, suppose I have a And proved a 
circle before me, I observe its radii ; I see ^^''°'"^- 
that they are equal to each other, or at least more 
nearly so than any difference that I can measure by 
my eye. I start with the hypothesis that they are 
equal, and measure them ; this is a posteriori method 
of proof. It can, however, never approach to any thing 
more than something less than any measurable differ- 
ence between the radii. But by a priori demonstra- 
tion we can prove that they are equal as a fact, because 
of necessity they must be so. 

843. So too with the Formal property of any spe- 
cies. The web-feet of aquatic birds, for instance. We 
may conjecture from the examination of such Modai proper- 
feet that they are designed for swimming ; conjectSed ^l 
and hence indicative of the Modal property ^^^°^^' 
" aquatic," as applied to birds. We form the hypo- 
thesis \_jingo hypothesin\ " that web-footed birds are 
aquatic." We appeal to observation — that is, we inves- 
tigate the hypothesized predicate a posteriori^ and find 
it true. 

8M. Then Analysis of the class-conception, further 
Inquiry and Observation, Measurement, Calculation and 
the various other Methods of Investigation, will give 
us further predicates to the subject. We will therefore 
proceed to treat these Methods separately. 

SECTION II. 
Of Observation and Testimony. 

845. Observation is the first and most primary of 
all the Methods of Investigation. From the moment 
that we open our eyes upon the objects of this world, 
we begin to be observers of what is taking place in it. 



224 LOGIC. — PAitT n. [chap. 

Each of our Senses is an avenue through which infor- 
mation is constantly coming in. 

846. But of the psychological powers and of the 
grounds of belief in what we thus observe, it is not 
my design to speak here. We all perceive external 
objects, we form conceptions of them immediately, we 
cla-ssify them, we believe in their reality, and never 
do or can seriously distrust the testimony of our 
senses. 

847. Our primary Method of obtaining a know- 
observation the ledge of the facts and events of the external 
thoT'^ ^' world, and of the properties and relations of 
the objects existing there, is Observation, When by 
our own agency the facts which we wish to observe 
are either brought into existence or under our observa- 
Experiment. tiou, thc Mcthod is callcd an Experiment. 
Experiment, therefore, is a Method of Investigation 
differing from Observation only, in the purely acci- 
dental circumstances of the observed fact having been 
voluntarily produced by ourselves for the purpose of 
the Observation. 

848* For the observation of the facts of the external 
or material world we have the five senses : Sight^ 
Means of Ob- Touck^ Hearing^ Smelly and Taste, For the 
servation. facts of thc intcrior world, those which pass 
within the Soul, we have the single faculty or interior 
sense called Consciousness, 

849. In both these cases the same faculty gives us 
Subject and botli the Subjcct and the Predicate included 

as^one^ "" ^^^"^ lu tlic ouc pcrccption, and wdth the intuitive 
judgment afiirming the one of the other as property of 
a Subject. Tims, I see a rose and that it is red, I smell 
that it is fragrant, I touch that it is soft and velvety. 
I am conscious of thinking, and that my thought is 
dull or active ; I am conscious of admiring, and that 
my admiration is profound ; I am conscious of envy, 
and that envy makes me unhappy. 

850. From these intuitive perceptions of the senses 
there is no appeal, or if there is there is no means of 



II.] METHODS OF INVESTIGATION. SECT. H. 225 

settling that appeal. One sense may indeed sometimes 
correct a judgment based upon another. ^^ ^ppea 
Thus, by a touch I may find that what I {I?f s^n^se^'per: 
had supposed from sight alone to be a peach, ^eptions. 
is but a piece of stone so carved and colored as to look 
precisely like a peach. But in this case it is only one 
sense acting in its appropriate sphere, furnishing means 
to correct the too hasty judgment based upon the data 
furnished by another. Nor is there any reason to trust 
one sense any more than another, when each are exer- 
cised within their appropriate spheres. 

851. So with consciousness. If I am conscious of 
believing, or doubting, or remembering, there no appeal from 
can be no appeal from my consciousness, consciousness. 
The fact may be miscalled. Thus, I may call the feel- 
ing of which I am conscious humility, when all others 
will see that it is but spiritual pride. The mistake, 
however, is in the name and not in the fact that I have 
some feeling. 

852. The Predicates of any Subject may express 
either (1) the Implied Properties affirmed in Matter. ex- 
Synthetic Judgments a priori, (2) Modal prScates"! 
Properties expressing the Final cause of any Property 
included in a class-conception considered as a Formal 
Property ; and (3) Accidental Properties denoting 
(a) that which distinguishes one individual from an- 
other, or {b) that which distinguishes an individual 
from itself in another condition or at another time ; 
(4) {a) the Cause, or (b) Effect, and (5) the Quantity. 

853. Now as all investigation begins with indi- 
vidual objects, a property when first brought to our 
minds cannot be referred to any of these classes ; for 
at first we do not know that it is any thing more than 
a separable accident, nor in fact do we know that it 
is not. 

854. In the course of our investigations we may oc- 
cupy either of two different positions in rela- investigation 
tion to the Subject. We may be investigat- of AutffiilS. 
ing it de novo^ or we may be merely following an inves- 

10^ 



226 LOGIC. — PAJRT n. [chap. 

tigation made by some one else before us. In this 
latter case we are learning from Testimony or Au- 
thority, from the Force of Terms or from the Common 
Sentiment of mankind. In all these cases we are 
not investigating the subject, but we are looking for 
the result of an investigation made by some one 
else. 

855. But if we are investigating the subject itself, 
and looking for properties and relations which are not 

obvious on the first sight, it will be found 
thesesin inves- ucccssary iu almost all cases to form some 
gation. hypothesis or conjecture of what this pro- 

perty is to be. This hypothesis serves something the 
same purpose as the a?, which is the representative of 
the unknown quantity in Algebraic Equations. Thus, 
suppose one is trying to discover the Cause of any 
phenomenon ; he would need to make a supposition 
beforehand, and proceed to test its correctness by facts 
and observations. Few discoveries have in fact ever 
been made except under the guidance of a shrewd 
guess, conjecture, or hypothesis of what the truth or 
fact is to be when it is found. 

Having noticed the principal Methods by which 
we can investigate subjects by the direct application 
of our faculties to the subjects themselves, let us con- 
sider Testimony, or the Means by Which we avail our- 
selves of the exercise of the faculties of others upon the 
subject of our inquiries. 

856. Of these we have two distinct classes : (1) Sub- 
jects which we might investigate directly ourselves if 

Kinds of Tes- ^c had the opportunity and means ; and 
timony. ^2) thc Prcdicatcs which depend upon Au- 

thority, or the expressed Will of another. 

857. For by far the largest part of what we know, 
or at least by far the largest part of the facts upon 
Tehtiroony as a which wc havc to dcpcud iu forming our 
ttif"^ oisfrvl opinions, constructing our systems, as well 
tions of others, g^g fop ^j^q practical purposes of life, we are 
obliged to depend upon the observations of others ; 



n.] METHODS OF INYESTiaATION. SECT. II. 227 

their statements of what has come within their expe- 
rience and observation is called Testimony, 

858. The use of Testimony supposes that others 
have the same faculties and means of know- The use of 
ing as ourselves, and opportunities which JJ/eropponS- 
we have not had. This fact, however, leads hav|'^St''\ld 
us to investigate the nature and value of ourselves. 
Testimony. And I shall at present speak of Testimony 
only by itself, referring to a subsequent Chapter in 
which I shall speak of the Concurrence of Testimony, 
as giving demonstrative force to simple Testimony. 

The value of Testimony is to be estimated Tests of the 

■i,ir»n • , A value of Testi- 

by the loUowmg tests : mony. 

859. (1) The nature of that concerning which the 
testimony is given. 

Some facts are obvious in themselves, easily seen, 
and not easily misunderstood — snow on the p^ature of the 
face of the earth, a mountain, a desert, a ^"^J®*^^ ™^"^'^- 
loud noise, and such like facts, are too obvious to 
diminish aught on that ground from the value of testi- 
mony to their reality. 

860. But in a large variety of cases, the fact is 
beyond the reach of human faculties, and that which 
is reported as the fact is merely the inference Reporting theo- 
from the fact. Thus, take all the reported "es for facts, 
cases of demoniacal possession, witchcraft, second-sight, 
&c. The fact really testified to is beyond the reach 
of the senses — a mere inference from what was seen. 
One might see that another was acting strangely and 
report those acts, but to see that there was demoniacal 
possession, the presence of the spirit of one departed, 
or any of that kind, is of course quite impossible."^ 

861. So too in reporting the acts of another. A 

* Of course I am not questioning the reality of such facts, and espe- 
cially demoniacal posisessions wliem properly vouched for. Tlie testimony of 
our Lord in the New Testament is of course that of a competent witness. 
But for all persons who have nothing heyond the ordinary insight of mor- 
tals, the demoniacal possession, witchcraft, &c., must he only a theory to 
explain the ohserved facts. 



228 LOGIC. — PART n. [chap. 

witness might speak of his motives as facts that he had 
Motives for obscrvecl, and testify that such a person was 
the acts. angry, or jealous, or benevolent, &c., when 
the moral states could be nothing more than inferences 
from what was seen. The facts which could be seen 
and testified to, and the inferences from those facts, 
must be carefully distinguished. 

862. (2) The intelligence of the witnesses. In many 
cases this is of slight importance, since the fact may 

Intelligence of ^c SO obvious as that uo ouc could mistake, 
the witness. g^^- j-^ othcrs it Is far otherwise. The testi- 
mony of a physician, for instance, to a disease with 
which an invalid is suffering, would be of vastly greater 
value than that of one who knew nothing of medicine, 
and had scarcely ever seen a sick person in his life. 

863. (3) Opportunity to know is reckoned as one 
of the fundamental points in the value of testimony. 

Opportunity to One should spcak of what he has heard and 
know. seen. If he only reports what he has heard 

others say of what they have heard or seen, the testi- 
mony becomes of constantly less value at each remove 
from the original witness. 

864. (4) Integrity or moral honesty in the witness 
Moral charac- is of coursc au important element in the 

ness*? ^ ^^' " value of testimony. Without it the witness 
may be only imposing upon us the fictions of his own 
imagination instead of any outward realities. 

865. (5) And finally, since there are but few if any 
persons without some prejudices, feelings of personal 

Freedom from intcrcst or passiou, or attachments to theory, 
prejudice. wliich wiU vcry much influence the value 
of testimony, it is seldom if ever safe to take the testi- 
mony of any one without knowing something of his 
animus in regard to the subject-matter, and guarding 
against its influence upon the testimony itself There 
is scarcely any event or fact that has not two sides to 
it, and its appearance will depend very much upon the 
side which is presented to us, or from which we choose 
to view it. A traveller with aristocratic notions. 



11.] METHODS OF INVESTIGATION. SECT. H. 229 

travelling in Europe, and constantly received into 
aristocratic circles, and receiving the kindest civilities 
from that class of the population, seeing every thing 
from their position and with their eyes, would report a 
very diflerent class of facts from one who should walk 
on foot, associate with " the toiling millions," and see 
life as it passes with them. 

866. We must also remember that testimony to be 
of any value must be positive. More mis- Testimony must 
chief has been done by the neglect of this ^^ positive, 
fact, obvious as its importance is, than one would at 
first believe. 

A good illustration of this mistake is seen in the 
case of the Irishman, who is said to have complained, 
because he was convicted on the testimony of one wit- 
ness^ who saw him commit the offence^ when there vrere 
hundreds that did not see him commit it. 

867. Omissions of this kind are most likely to occur 
in the midst of statements, where other cir- omissions 
cumstances or occurrences are mentioned. jYkd? to"^^- 
Thus a very common case, in theological ^"'^• 
controversy, is in the testimony of an ancient Father, 
that " in Alexandria, from the days of St. Mark, the 
Presbyters were accustomed to select one of their 
number, place him on the throne, and call him their 
Bishop." No mention is here made of his having been 
ordained, as a part of the process by which he was 
placed in the otifice of Bishop, and hence it has been 
argued that there was no ordination. 

868. The mere omission to mention the occurrence 
of what was customary, is no proof that it . . 
did not occur. History, from the necessities testSJonT o? 
of the case, is full of such omissions. It is 
impossible to state all that occurred, and if it were 
stated no one could read the books that would be 
written, nor could the world contain them. 
Hence writers do not usually mention that most \keiy ^t^ 

T . T . A.\^ 1. '1. ' be omitted. 

which IS SO common as that it is never 

omitted, and is perfectly well understood by those to 

whom the writings are addressed. 



230 LOGIC. — ^PART n. [chap. 

869. Bat even positive testimony to a negative pro- 
positive Testi- position can never be equal to positive testi- 

?atf/e^ropost niony to an affirmative one. Positive testi- 
tion. mony to a negative proposition, like negative 

testimony, is for the most part only the absence of 
testimony. 

870. Positive testimony, supposing there is no 
fraud or mental hallucination, can be accounted for 
only on the ground of the reality of that which was 
seen, heard, &c. Testimony to a negative, however, may 

always be accounted for on the ground of in- 
timoly. how It ability or inattention on the part of the wit- 
ness, as well as by the absence of that which 
he did not perceive. If, however, one man should 
testify that he had seen an extraordinary phenomenon, 
and a large number of others — even two or three other 
persons, having their attention directed to the same 
object or place, and occupying a position equally 
favorable as that of the man who pretended to see it — 
did not see it, this conflict of testimony would always 
raise the question of the sanity of the mind and facul- 
ties of the affirming witness, over and above the ques- 
tion of his veracity. In all such cases the contradiction 
in the testimony must be in some way accounted for 
before either can be received, unless it be in cases 
where one side is vastly preponderant against the 
other. Such a disparity may in itself, unices it can be 
accounted for otherwise, be taken as a sufficient gua- 
rantee of the accuracy of the testimony on that side. 
But in all these estimations, ceteris paribus^ the pre- 
ponderance is always on the side of the affirmative 
testimony. 

871. Again, we must always distinguish very care- 
Fact and infer- fully between what is seen and the inference 

Fact. '^"* ' ® from it. Perhaps there is no case that illus- 
trates this so well as the common belief and testimony 
to the fact that the sun rises and sets. The fact is a 
relative change in position — the motion of the sun is 
but an inference or a theory to account for that fact. 



n.J METHODS OF INVESTIGATION. SECT. H. 231 

The fact we take as indisputable, the theory we reject 
whenever we can show that there is a better one or that 
it is unnecessary. 

872. The truth of a jpriori propositions we con- 
ceive to be independent of any Will or of any Mind 
even. They are necessary truth, and therefore abso- 
lutely true. Their truth depends upon no Testimony not 

-••i, . 1. i. TT • "NT ^sed in Neces- 

condition whatever. Jtience, m JN ecessary sary Matter. 
Matter we seldom make use of Testimony, or the 
authority of others. 

873. But with regard to physical truths, although 
their being true depends upon the Will of j^ physical 
the Creator or First Cause of them, yet we mony^o Facts 
know the Predicate from an observation of **°^- 

the Subject itself. We have but to look at a rose to 
see that it is red, to taste an orange to see that it is 
sweet, &c. From this observation of the properties in 
.the effect, we infer the intention or will of the Intelli- 
gent Cause, which is the Creator. In Physical Matter, 
therefore. Testimony can be properly used only to 
facts. It can never establish theories or opinions, but 
only facts ; the fact that this, that, and the other 
man held the theory, and upon what grounds he 
held it. 

874. But in Moral Matter we can never learn the 
properties of subjects by any mere investigation of the 
subject itself. They depend upon the will Testimony in 
of him from whom they proceeded. Of S^o"^^ Author? 
these things, therefore, our only means of ^^^• 
knowledge is the Testimony of some one who knew the 
will and intention of the Authority from which they 
emanated. Thus, in Revelation we have Sacrifice, 
Baptism, the Holy Eucharist, the Lord's Day, &c. 
Of these no one knows or can know what is to be pre- 
dicated of them in certain respects except from Reve- 
lation itself. And Revelation is a Testimony to the 
Will of God concerning those elements of Religion. 
Of Baptism, for instance, we can know what it is ; how, 
by whom, and to whom, it is to be administered, and 



232 LOGIC. — PAKT n. [chap. 

what is its efficacy upon the worthy recipient, only 
from the Scriptures. AH of these are questions that 
never can be answered by any study of the subject. 
Baptism, itself; but only by a study of the Revelation, 
which is Testimony to the "Will of God concerning it. 

875. So it is in every society and organization of 
Positive insti- mcu. Thcrc are, and of necessity must be, 

tutions )ji all ... ' ^ j * ...'■ , . / 

societies. somc positivc rulcs and institutions not 

dependent upon any one's sense of propriety, but 
ordained by the consent of the collective whole ; or at 
least by the authority tliat acts for that whole. And 
these statutes, constitutions, canons, by-laws, &c., by 
whatever name they are called, become the Testimony 
by which we investigate the properties which may be 
predicated of the subjects treated of in those docu- 
ments. 

876. Again, Lexicons, Dictionaries, and such like 
Dictionaries compilatious, are Testimonies which we use 

Ihtmelmnglf ^s a mcaus of investigating the meanings 
words. ^j^^ definitions of words. Analysis is often 

of great service. When a word is compounded of two 
or more, or is used in a derivative form, we can often 
get an important suggestion towards its meaning from 
an analysis of the word into its parts — or as gramma- 
rians say, from its Etymology. But the real force and 
meaning of a word after all will depend upon the usus^ 
loquendi ; and a Dictionary or Vocabulary is but a 
Testimony to that usage of a language which deter- 
mines the meaning of words. 



SECTION III. 

Of Measurement and Calculation. 

877. Measurement as a Method of Investigation 
requires a mention, although there is but little to be 
said of it. It is the Method by which we find the 
Predicates that answer the questions " how many ? " 
" how much ? " " the time when ? " &c. 



n.] METHODS OF INVESTIGATION. — SECT. m. 233 

878. We may have a definite answer, or only an 
indefinite, or comparative one. Thus, if one 

ask how high Mont Blanc is, he may obtain compafative 
the indefinite comparative answer, " It is 
the highest of the Alps." Such answers give of course 
but indefinite answers, by comparing the thing which 
is unknown to the inquirer with something which is or 
is supposed to be known to him. 

879. But for a definite answer in Quantity, it is 
always necessary to assume some unity or Assumed unit, 
standard, and to give the answer in the number of 
the units of the assumed standard, comprehended in 
the object to be measured. Hence we have our tables 
of unities in long measure, as " inches," " feet," " far- 
longs," " miles," " leagues." We have also unities of 
measure in time, in weight, in solid quantity, &c. 

880. Some such Method is, I apprehend, that which 
in fact gives us the first hypothesis, or hypo- Measurement 
thetical knowledge of the implied properties fearniS^im^ 
of the subjects treated of in the sciences of ^f^Ge^oSi^^ 
Continuous Quantity, Geometry, Trigono- ^^s^''^^- 
metry, &c. Such implied properties there are in every 
class-conception. They are likely to be brought to our 
knowledge first by some one of the Methods of Investi- 
gation (and may be brought to our mind by any of 
them). But when they are so brought to our minds, 
they must be proved by Demonstration, which we have 
treated as one of the Methods of Proof. Thus, I may 
learn at first /V^^ttz. actual measurement^ that the square 
of the hypothenuse of a right-angled triangle is equal to 
the sum of the squares of the two other sides, and then 
prove it as a necessary and invariable property of all 
right-angled triangles a priori. Such, I suppose, has 
been the method in which most of the Predicates that 
are now aflirmed a priori were first discovered ; they 
wef e first learned a posteriori by observation or mea- 
surement, and then affirmed on a priori grounds. 

881. It is not, however, the Method of their Dis- 
covery but their Proof which determines between the 



234 LOGIC. — ^PAET n. [chap. 

Synthetic Judgments a posteriori and those which are 
a jpriori. 

882. When the question relative to quantity is, 
Counting a ^' how manv ? " we have as preparatory to 

Method of In- n ^ , . •^^^ j • 9? r r J 

vestigation in calculation " coununo' as a means oi enu- 

Discrete Quan- ,. ,t i r» • t • t t • 

tity. meratmg the number oi individuals m any 

Logical Whole. In this case the unity is not assumed 
but is given. It is the logical individual. 

883. Arithmetic, Algebra, and the Calculus are 
Methods of but Methods of Investigation in Discrete 

Calculation. Quantity. They presuppose counting or 
enumeration by individuals as units of number. 

884. Of course we cannot go into a consideration 
of these Methods in detail here. To do so would 
require a Treatise on Arithmetic, Algebra, and the 
Calculus. I will in this place therefore specify only 
what is essential to all of them. 

885. The Methods described in the works on these 
Methods, in subjccts, are determined rather by \h.^ Idea 

detlrmS^by of thc Uscful thau by the Idea of the 
Useful ^ ^^^ True. They all come to the same result, 
and the superiority of the one over the other consists 
in its superior usefulness ; that is, it is a shorter and 
more useful way of doing what may be done in some 
other way. 

886. So far as the Idea of the True determines 
them, there are but two radically distinct Methods of 

Logically but Calculation : (1) when the parts are given 
two Methods, to gj^(i the whole ; and (2) when the whole 
with some of the parts are given to find the other, or 
others if there be more than one. 

887. For the first Method or Addition it is neces- 
conditions of sary that all the parts be given : one of them 

thod. "^'^ ®" at least a Discrete Quantity ; and the others 
so as to be ascertainable by means of the one fhus 

given ; thus, - + _ + 4 = a?. 
2i o 



n.] METHODS OF INVESTIGATION. — SECT. IH. 235 

In this case the three terms - + - + 4: are the parts, 

and X represents the whole, which is still an unknown 
quantity. By the Method of Addition we find that 
quantity and substitute it for x, and say x = 24, or 
twenty-four is the whole."^ 

* As illustrating this point we may refer to the old Sophism of AchiUes 
and the Tortoise. — " They start at the same time from points one mile 
apart, the Tortoise heing ahead. While Achilles is running that mile the 
Tortoise will have run one-tenth of a mile. But while Achilles is running 
that one-tenth of a mile the Tortoise will have run one-tenth of one-tenth, 
that is, one-hundredth of a mile, and so on ; therefore AchiUes will never 
overtake the Tortoise." 

Leibnitz first proposed as a solution of this sophism, and it has been 
repeated by Coleridge and De Quincey, that it implies the infinite divisibility 
of space, without taking into account the equally infinite divisibility of time 
also. I am not authorized to say that this solution is not satisfactory, I sup- 
pose, but I really cannot see that it has any meaning that is to the purpose. 
Whately says that Aldrich and the old Logicians answered by proving that 
the Conclusion is false. But as he justly remarks that is no answer, if the 
Premises are admitted and the Formula is unquestionable. Whately an- 
swers by saying that the Argument cannot be stated Logically at all ; that 
is, in any Logical Formula. But to this we reply, so much the worse for 
the Formulae. If there is, as he admits, " a seeming demonstration," there 
must be a Formula to which it can be reduced, though it may be of course 
an invahd Formula. Otherwise it must be reducible to a Formula valid 
in itself, without fulfilling the conditions of that Formula. 

The Sophism can be reduced to a Categorical Formula as well as any 
other Algebraic Equation. The expression in these Formula is awkward 
and unnecessary. Mathematics is the Logic of Continuous and Discrete 
Quantity. Nor is there the slightest necessity of bringing their arguments 
within the Formula of Logical Quantity. But if one will insist upon such 
a statement of the Sophism before us, it will then be found that the word 
" while " is used in each successive Premise in different senses. Hence 
the Fallacy of Ambiguous Middle. 

Thus, — The first period is '^ whUe ; " 
'* While " is the second period : 
.*. The first period is [equal to] the second. 
That is, it takes as long to run the mile and the tenth, as it does the tenth 
and the hundredth — and if so AchiUes wiU never overtake the Tortoise. 

But in the Methods of Discrete Quantity the fallacy is in requiring a 
Whole without giving any measure of the parts. The Whole is " the 
quantity of time from the moment of their starting until that of their over- 
taking." Now undoubtedly the time of AchUles running the mile is one 
part of that Whole. But its value is not given either relatively to the Whole 
nor in Simple Quantity. So, too, the time of nmning the tenth and the 
one-hundredth is a part of the Whole ; but we are not told what part, nor 
how long it is in Simple Quantity. 



236 LOGIC. — PAKT n. [chap. 

880. If there are two unknown quantities, the Me- 
thod of Adding is different ; but the Method of Inves- 
tigating the Discrete Quantity of the Whole, or finding 
the Predicate is the same, namely, it is Addition of 
the Parts. 

889. Or again, if we have a Whole and some of its 
second Method. Parts givcu, to find the other part, we have 
the Method of Subtraction. Thus, 

6 — 3 — 2 = a?. 
Here 6 is a Whole, and 3 and 2 are parts of the 
Whole, and x represents the other unknown part which 
is to be found. By Subtraction we find it and say, 

aj = 1. 

890. But Multiplication, Division, Involution, Evo- 
Muitipiication, lutlou, &c., &c., arc ouly more useful be- 
Division.&c. cause shorter Methods to the same results; 
that is, to find a whole from the given parts, or a part 
from a whole — the rest of the parts also being given in 
Discrete Quantity. 

891. When I speak of the parts and the whole, &c., 
being given, I mean that they are virtually given. As 
The Parts how ^^^ ^^ A^^t cxamplc abovc one part alone was 
given. given in pure quantity, 4 ; but it was given 
in such a way that the value of the others could be 
obtained from it. It was given, and its fractional value 
in relation to the whole was also given. And this will 
always be found to be necessary. If the parts are not 
given in simple quantity they must be in or reducible 
to some fraction or multiple of the whole. 

892. The whole must of course also be homogeneous. 

Parts must be Tlius, if we add 6 and 8, the whole, as all 

homogeneous, ^yholes lu purc quantity are, is homogeneous. 

Now from sucli a statement we can simply have no answer, because 
the Premises are inadequate. But the Sophism instead of saying as it 
should, that there is no answer, gives a negative answer, which is of course 
a very different thing. 

But let us give a value to either of these parts and the answer is easily 
obtained. Suppose that Achilles runs at the rate of twelve miles an hour, 
and an acquaintance with the first principles of Algebra is all that is 
required to find the answer. 



n.] METHODS OF INYESTiaATION. SECT. IV. 237 

It is merely 14 — not fourteen men or fourteen dollars^ 
or any thing of the kind, but fourteen simply. 

893. But if we have six men and eight dollars^ we 
cannot add them into a whole, which will be 
expressed by any name in the EnMish Ian- produ?ffS 

•*• CI 1. 1 • er Whole. 

guage. buppose, however, we have six 
horses, eight cows, twelve sheep, we may add them, 
and then the homogeneous whole is not horses, cows, 
or sheep, but it may be denoted by a generic term 
including these parts as species. Such a term is the 
English word, " cattle " or " stock." 

894. And for the same reason in Division the divisor, 
and in Multiplication the multiplier, must be ^i^igoj. ^nd 
pure number; while the dividend and the Sl^^pure^^m- 
multiplicand may denote any objects in Lo- **®^- 

gical Quantity."^ 

SECTION IV. 
Of Average and Exclusion. 

895. It is sometimes the case that we cannot obtain 
an exact observation of a fact which we wish ^he use of 
to use in our calculations. And again, there ^^®^a^e- 
are many facts differing from each other in many 
points, that are either based upon and indicative of 
a law, or at least afford results of great importance, 
which, however, none of our inductive processes can 
reach. Such facts and results are obtained by what is 
called the Process of Average. 

896. Average is obtained by adding together seve- 
ral results, and dividing the amount by the how obtain- 
number of results — these results must of ^^^ 
course, therefore, be stated in Discrete Qu.antity. 

* The Method of investigating or calculating Probabilities has neces- 
sarily been anticipated in the preceding Part, p. 87 et seq., 157 et seq. The 
justification for such an anticipation is in the fact that the amount of pro- 
bability is in these cases an essential part of the Copula, and therefore im- 
plied in the formation of the Judgment, as much so as the inclusion of the 
Subject in the sphere of the Predicate in Pure Categoricals, the Sequence 
in Conditionals, or the Excluded Middle in Disjunctives. 



238 LOGIC. — ^PART n. [chap. 

897. For example, the mariner at sea is desirous 
of getting the precise position of a heavenly body. 

Observations But from tho rocking of his vessel it is im- 
atsea. possiblo to get two observations precisely 

alike. Let him take several and take the average. 

898. Again, suppose we wish to ascertain the pres- 
sure or weight of the atmosphere. We find that the 

In the use of Baromcter does not indicate exactly the same 
the Barometer, ppessuro twicc pcrhaps in a whole month. 
Heat, the time of the day, the currents of the atmo- 
sphere, all affect it. But let there be made observa- 
tions several times a day for a year, for instance, add 
them all together, and divide by the whole number, 
and we have an average approaching the truth, just in 
proportion to the extent of the observations. 

899. This Method is of vast importance in the col- 
lection of Statistics, and has given us some of our most 

In collecting uscful facts and estimates in Political Eco- 
statistics. nomy, in the doctrines of Insurance, and in 
fact in every department of business and of legis- 
lation. 

900. Thus it is found by Statistics that out of every 
one hundred thousand infants born in England and 

statistics of Wales, fifteen thousand die the first year. 
Deaths. gyg thousand more in the second, about one 

in four of the whole number before they would have 
reached their sixth year, and scarcely one-half reach 
the age of forty years. Now suppose results similarly 
obtained from other places, other races of people, other 
modes of treating their infants, to differ in the propor- 
tion of deaths from those in England and "Wales, we 
should have this difference as a fact to be accounted 
for, and its investigation could scarcely fail to lead to 
knowledge of the greatest importance. 

901. In the same way Physiologists, by dividing 
vitabiiity. the whole number of population between 
certain periods, of five years say, as from twenty to 
twenty-five, from twenty-five to thirty, and so on by 
the number of deaths of persons of that age, obtain a 



n.j METHODS OF INYESTIGATION. SECT. IV. 239 

number which will of course vary with the proportion 
of deaths to the whole population. This is assumed to 
represent what is called the vitability'^ of men and 
women, during these different periods of their life. In 
some of these periods the vitability of the males is greater 
than that of the females, as from fifteen to twenty, and 
from forty to forty-five. In others that of the males is 
greater than the females. In this way definite results 
are obtained, which are of the greatest value in the 
investigations of many of our most useful as well as 
interesting sciences. 

902. Even those matters which are supposed to 
depend chiefly upon the will, such as mar- m moral mat- 
riage, and suicide, are found to yield results ^^^• 
astonishing from their uniformity. Quetelet,f the Bel- 
gian statistician, affirms that the Belgian people pays 
its annual tribute of marriage with more regularity 
than that of death. Not only does the total Marriages, 
number of marriages, as well in towns as in the coun- 
try, follow a constant mathematical law, but the same 
regularity is observed in the numbers which indicate 
the marriages between bachelors and maids, bachelors 
and widows, widowers and maids, and widowers and 
widows. So in respect to the ages at which marriage 
is contracted, there is an astonishing uniformity in the 
annual returns. In regard to suicides the statistics of 
France J for a period of twelve years exhibit suicides. 
a similar uniformity. Their number varies but little 
from year to year. It is less in December than in 
any other month. From December it increases to 
June, when it attains its maximum and then diminishes 
regularly until December again. 

903. These facts, which can be obtained in a form 
to be of use by the Method of Averag-e 

TTT.T.i ..V Imply causes 

only, doubtless imply some causes extrinsic extrinsic to the 
to the will of man, and which therefore are 



Will 



* Carpenter^s Human Physiology. f ^'^ Systemc Social, p. 67. 

X Axmuairo de rEconomic Politique, 1851, p. 200. 



240 LOGIC. PART II. [chap. 

within the legitimate sphere of scientific investigation. 
They furnish a case for the Methods of Elimination 
(Section VII. below). 

904. Now where there is uniformity in results, 
there must be of course a cause acting under a law or 

Uniformity in from somc scttlcd dcsigu. And in the case 
this law. Qf intelligent causes, the design itself gives 
the law to its activity and determines it. But in Na- 
ture, where the Causes are considered as mere Forces, 
acting without intelligence of their end or of their law, 
uniformity is always considered primarily and espe- 
cially as implying law — an unchanging rule guiding 
the activity of the Force. 

905. In this view, the Average of a single series of 
figures might indeed be valuable in many cases, as 

Comparison of thosc for iustancc specified in 889 and 890. 
Averages. g^^^ g^i^ i|g great valuc as a Method can be 
seen only in its application for the purpose of com- 
paring the average results of different series of figures 
relating to the same matter, at different times or under 
different circumstances, as in the cases specified 
above (894). 

906. The Method of Exclusion is used for abridging 
processes of investigation by the exclusion of whole 

Method of Ex- classes of objects as individuals from the 
elusion. necessity of examining each one separately. 

The exclusion is effected by means of properties assumed 
as differentia of species, and may be of two kinds. 

(1.) The exclusion of one fact or species of facts 
First variety, after auothcr from any given Predicate 
assumed as the Differentia of a species, in order to 
include a remaining fact or class of facts in the sphere 
of that Predicate. 

(2.) The exclusion of one fact or subspecies of facts 
Second variety, bclouging to any Proximatc Genus from one 
after another of the coordinate species in that genus, 
in order to include it by this means in some one 
remaining species. 

907. The first makes or implies a statement in the 



n.] METHODS OF mVESTIGATION. SECT. lY. 241 

form of a Disjunctive Judgment with the Based upon 
Predicate common and the Subjects coordi- Judgment" with 
nate, as either A or some non-A is B [410]. feels '""^'^ ^''^' 

908. The second of these varieties makes or implies 
a statement in the form of a Disjunctive n,- inn.t.v^ 
Judgment with the bubject common and the cSnatVpre^ 
Predicates coordinate, as A is either B or C, f^j^ates. 

or D, &c. [408]. 

909. This Method has been called the Abscissio 
Infiniti^ and is of great use both in investi- 
gation and in proof It partakes in fact so sio\njinitu^^{s 
fully of the Differentia of both classes of Me- '^^' 
thods that we are in doubt with which of them to place 
it in our present Treatise. We put it here, however, 
because we are treating of Methods of Investigation 
before Methods of Proof. 

910. Perhaps the best illustration of the first form 
of Abscissio for our present purpose, is the mustration of 
one which we have already made use of in the first variety, 
examining the validity of Moods and Figures of Syllo- 
gisms [478 et seq,}. Thus we said (or rather used the 
implied Disjunctive), " Either those with negative 
Premises, or some of those that have not both Pre- 
mises negative, are valid," we completed by the modus 
toUente jponens ^ proving that those with negative Pre- 
mise could not be valid. We then divided the re- 
maining coordinate, " those which have at least one 
Premise affirmative," into two coordinate parts, and 
said or implied again, " Either those with Particular 
Premises," or " some of those whose Premises are not 
both Particular are valid ; " and proceeded as before 
until we come to the species of which alone '' validity " 
could be predicated. 

911. In this case we knew at the outset that some 
of the individuals included in the divided 

whole — that is, some syllogisms, were valid, may'^be ^used 
But if we had not known this we could even Disjinctfve ' is 
then have proceeded in the same method 
until we had found that there T^as no individual in the 

11 



242 LOGIC. — PART n. [CHAF. 

divided whole of which '' valid '^'^ could be predicated. 
In that case we should have ascertained that " valid " is 
a Differentia incompatible with the Essentia, which is 
constitutive of the Logical Whole as a genus ; that is, 
with the Material Properties of the Logical Moods. 

912. But in this case there would have been only 
the form without the reality of a Disjunctive Judg- 
ment. The Disjunctive would have been merely sup- 
posititious, designed or supposed for the sake of the 
Method, since a true and valid Disjunctive always im- 
plies that one member at least shall be true. 

913. This Method is often of great use as a Method 
of Proof in Geometry. Thus in the Theorem, " A line 

Used in Geo- ^^^ ^^1 from any point perpendicular to a 
metry. straight line, is the shortest distance between 

the point and the line. For either the perpendicular 
is the shortest line or some not perpendicular is the 
shortest." But as the perpendicular makes a right 
angle with the line, any other line would be the 
hypothenuse of a right-angled triangle, of which the 
perpendicular is one of the legs. Hence no non- 
perpendicular line is the shortest. Consequently the 
perpendicular is the shortest. This Method is of course 
vastly shorter than that by which we prove of each 
possible line, not a perpendicular, separately — that it 
is not the shortest. 

914. But let us now take a case of the other kind. 
Illustration of in which wc have an individual or several 

the second va- « . ^ . -, -j . « 

riety. lormiug a sub-species, ana are desirous oi 

finding to which of the species it belongs — in short to 
find what it is. 

915. Let us take for an. illustration a case of 
chemical analysis. We there say this is either an 
acid or an alkali. We test it and find, let us sup- 
pose, that it is not an acid. It is therefore an alkali. 
We must say this is either potassa, or soda, or am- 
monia, &c., enumerating all of the alkalis. We pro- 
ceed as before and test it for potassa, for soda, &c., 
until by proving that it is not one or the other in turn, 



n.] METHODS OF INVESTIGATION. — SECT. V. 243 

we come to the last. But of course it is quite possible 
that we shall find which species of alkali it belongs to, 
that is, what kind of an alkali it is, before we have 
tested it for all. Or again, as in the former case, we may 
test a metal, for instance, for each of the alkalis in turn, 
and disprove each member of the supposed disjunctive 
in turn, and thus find that it is not an alkali at all. 
Here, as before, the Disjunctive form was merely sup- 
posititious — made for the occasion, without knowing 
before-hand that the individual was included in the 
Logical Whole at all. 

• 

SECTION V. 

Of Analysis, 

916. We may have two kinds of Analysis : (1) An- 
alysis of the Conception, and (2) Analysis of 

the Object of that Conception. The former con%lp?ions & 
is Logical Analysis and the latter is Pliy- '^^ ®^ •'®*^^^- 
sical Analysis. 

917. We have seen that every conception of a 
reality contains as its matter certain proper- The Matter of 
ties of that reality. These properties make conceptions. 
up its Essentia and Differentia ; its Essentia as includ- 
ing it in the next superior Natural Genus (thus show- 
ing what it is) ; and its Differentia limiting or deter- 
mining its reality by showing what it is not ; — thus 
giving the boundaries that separate it from other 
objects. 

918. The Analysis of this Conception therefore 
gives us each of these properties as separate ^he Analysis 
predicates, which may be affirmed of the gL^Sf preT- 
conception of the object as a Logical Sub- j^ectpfthecon- 
ject, and consequently of the object itself, '^^p^^''"- 

if the conception justly and properly represents it. 
Thus we may say of a triangle, " it has three sides ; " 
since three-sidedness is necessarily included in the 
conception of a triangle. 



244 LOGIC. — PAKT n. [chap. 

919. So too in Contingent Matter. The Matter of 
any superior and comprehending genus is always con- 

Anaiysis of taiucd iu thc conception of a lower and 
cSS^'nTMaf- comprehended species, and it may therefore 
^^^- be evolved as a predicate to that conception 

by Analysis. Thus I may say of a tree, " it is a vege- 
table ; " of an ox, " it is an animal," &c., since " tree " 
and " ox " are but species of the proximate genera 
" vegetable " and " animal." Or we may predicate 
any one of the essential properties of the higher genus, 
as of animal, the circulation of the blood — of the tree, 
its growth from a seed, &c. 

920. So far as Predication on the ground of Ana- 
lysis is concerned, it is of but little if any consequence 
how the conception which we analyze was formed. 

^ It may have been that which we formed in- 

Elements of a ^ • i • i r> i * n 

concepti'n may stinctivelv ou our iirst compansou oi one 

be Predicated i • , •, i ,i 'j i ^ 

of the concep- oDjcct With anotucr, or it may have been 
that more elaborate and scientific class-con- 
ception formed by scientific investigation. In either 
case we may analyze the conception, consider the ele- 
ments of which it is constituted separately, and sepa- 
rately they are Predicates which we may affirm of 
either the class-conception or of any individual com- 
prehended under it. 

921. The only possibility of mistake is in the forma- 
tion of the conception itself. If the judgment is untrue 

the conception was ill-formed. Thus, if I 
je"t.of th/con- should Say that " horses have wings," the 
SfnieStion be judgmcut would show that my conception 
a equate. ^^ ^^ horsc " was inadequate or erroneous. 
Or in popular language, one would say that I did not 
know what I was talking about. 

922. But in Geometry, the Mathematics of Con- 
tinuous Quantity,"^ we speak only of the conception ; 

* In Mathematics we deal with the conception exclusively. The very 
names which we use denote the conceptions and not the diagrams. But in 
what is called contingent matter it is not so. The names denote the indi- 
viduals as they are in the reality of being or existence. With these the 



n.] METHODS OF INVESTIGATION. — SECT. V. 245 

and that conception is one which we have formed in our 
own minds a priori, and by a conscious pro- m Mathematics 
cess of construction. Hence in our analysis S? ' e??or?eoiI 
of such conceptions we merely evolve what conceptions. 
we had consciously and designedly put into it, and 
there is no liability to error. Conceptions cannot be 
communicated from one mind to another. Each mind 
must form them for itself, "^ and as the process of form- 
ing the conception of a triangle, for instance, is the 
same in all minds, the conception itself of all geometri- 
cal figures must be the same in all minds. 

923. But informing class-conceptions of the objects 
in the external world, different properties of the objects 
themselves will seem most conspicuous and 
characteristic to different minds. Hence the erroT'^ln^con^ 
matters of those class-conceptions will be dif- '°°^" 
ferent to some extent, and may be different for each 
mind. Or if we undertake to reconstruct in our own 
minds the conceptions which others have formed from 
their description of the objects comprehended under 
that conception, the description never is and never can 
be quite adequate. Nor will it be understood by all 
minds alike. Every one has a conception of " apple," 
for instance, and yet who has analyzed that conception 
so that he can enumerate and describe precisely every 
element of its matter ? We can all tell an apple from 
a pear, but who can describe precisely and exactly all 
the points of difference between them ? Some of the 
most striking points all persons can give ; but no one, 
I apprehend, can give them all. 

924. The question will always arise, therefore, whe- 
ther the elements of our analysis be predicable of the 
individuals comprehended under our class-conception ; 

thouglits are occupied, and while in the former case we ignore the differ- 
entia between the diagram and the conception — in the latter the mind is 
chiefly occupied at first with those Formal Properties, and it is only by a 
slow process, and one that is at best liable to error and mistake, that we 
arrive at the class-oonception as it actually existed in the Divine Mind. 
* See Part II. Chap. IV. Sec. I. 



246 LOGIC. — PART n. [chap. 

not, however, in consequence of any fault or fallacy in 

Fah Cone ^^^ analysis, but on account of the doubt 

tions*^ ^oSce or Uncertainty about the formation of the 

of unintentional , . • . i /» a t 

false state- couccption itseli. Ancl many persons are 
^^^ "' charged with intentional falsehood when the 

fault is not the moral one of uttering what they know 
to be false. It is merely the misfortune of having so 
conceived the subject as that predicates which do not 
belong to it are included in their conception of it. 

925. This analysis of our conceptions is carried on 
Reason the bv the Rcasou itself: and the Reason pos- 

Agent of Ana- *^ n ia r- » * i i • i- j ' 

lysis. sesses a laculty oi insight or immediate in- 

tuition for the facts of consciousness, precisely as the 
external senses do for the facts of the external world. 
Thus, if I see that my class-conception of horse includes 
the property of solid-ungularity [having but one hoof 
. for each foot], I can no more doubt that my 
mate judle" of coucej^tion of horsc includes that property, 
Its correctness, ^j^^^ j- ^^^ ^^^ ^^ horsc bcforc mc has but 

one hoof for each foot when my eye is distinctly fixed 
upon the object itself. 

926. But let us pass to the consideration of the ana- 
lysis of the object itself. We cannot here give any pre- 

Anajysis of the ccpts or rulcs for accomplishing such analysis, 
object itself. Those rulcs are not and cannot be reduced to 
any simple system. Success depends to a great extent 
upon original gift. It is a matter of quickness of in- 
sight in the Reason, just as the perception of colors 
and of sounds is matter of difference in the constitu- 
tional peculiarities of the eye and the ear. No rules 
can be given which will enable one to distinguish 
between the different shades of color, or the different 
tones of the diatonic scale in music. If one cannot 
make the discrimination without rules, no rules will 
enable him to make it. 

927. In chemistry, however, analysis forms so large 

Rules and Me- ^"^^ SO indispcnsablc a part of its Methods, 

Natlfrai'" scf- ^hat thc rulcs and tests for analysis have 
ences. bccu cxtensivcly systematized and recorded. 



n.] METHODS OF INVESTIGATION. SECT. V. 24:7 

N"earl7 every science has done something of the kind. 
But the most that can be reduced to rule and formula, 
will in all cases be but a comparatively small part of 
what is to be done. 

928. An analysis of this kind is always an experi- 
ment, and the elements evolved are objects Analysis an 
of observation ; and we can of course predi- experiment. 
cate them of the object analyzed as having been con- 
tained in it. Thus common salt is analyzed into chlo- 
rine and sodium. Hence we may say, " common salt 
contains chlorine," — " common salt contains sodium." 

929. There is no appeal from the result of an ana- 
lysis. We may mistake the name of the sub- ^he certainty 
ject analyzed, and also that of the element of Analysis, 
given out. But the things themselves cannot be mis- 
taken. The greatest danger is in the too hasty infer- 
ence from the analysis. We may suppose Liability to 
the example which we analyzed was a fair "Mistakes. 
specimen of all the individuals of its class, and con- 
tained nothing which was not in them all and an essen- 
tial constituent, when in fact it was not so. Hence we 
may predicate of a class as one of its constituent ele- 
ments that which was only a foreign substance, acci- 
dentally in the specimen which we had subjected to 
our analysis. 

930. It is evident from these considerations that 
the analysis of any object may give us ele- 
ments of its constitution of which we were us e"ilmentf not 
ignorant before the analysis. Thus the 
analysis of water gives us hydrogen and oxygen. And 
it is especially characteristic of chemical analysis, that 
the elements evolved are totally unlike the compound 
that was subjected to the analysis. 

931. It will be observed that analysis can give as 
results nothing except that which was in the Analysis can 
analyzed compound. Thus if we analyze firfai """pro^r- 
water we get oxygen and hydrogen, and ^^^^• 
whatever else there may be in the water — but nothing 
more. Otherwise we have no certainty in our results. 



24:8 LOGIC. — PART n. [chap. 

932. But we often find on analysis what we do not 
and cannot find in analysis. This is especially true of 
the analysis of our conceptions. By the analysis we 

It enables us g^^ primarily merely what was contained in 
%xir ^p?opS- C)ur conception as the material properties. 
^^^^- But after the analysis has been completed, 

we are able to contemplate each element by itself, and 
also their relations to each other ; and thus we gain 
an insight of many imj)lied properties, which' of course 
were not contained in the conception. 

933. This distinction between what we get in an 
analysis and what we get on analysis, is very generally 

overlooked or omitted in speaking; of the 

The distinction ^ , rm •/;»•. • i j^i 

often overlook- rcsults. ihis, lor instaucc, is very constantly 
done by Cousin, who is certainly one of the 
most skilful and lucid in his analysis of all the meta- 
physicians that the world has ever seen. 

934. But as the conceptions which we form of 
The resuksof objccts iu thc reality of being are liable to 
i^onceptionV differ somewhat from those which existed in 

^uor differe^nt tlic Diviuc Miud bcforc their creation ; and 
""° ^' as the conceptions which one mind forms 

of objects in the reality of being will differ somewhat 
from those formed by other minds of the same objects, 
and as analysis of the conception can give only what is 
contained in the conception, the results of these analy- 
ses by different persons will be as various as their con- 
ceptions ; agreeing necessarily in some of their elements 
while they differ in others. 

935. So, too, that which may be expressly contained 
Material and in ouc mau's couccption as a material pro- 

ti^s^may^beTf- pertv lu continsrcnt Matter — that is, material 

ferent for difler- f i ^ y , i • t j • 

ent minds. to iiis conccptiou, may be only implied m 
another and vice versa, 

936. This results from the fact that our minds are 
Difference in impcrfcct and limited, " Yariasse est errorisP 

Anaiisi^" ° And there is probably no intellectual endow- 
ment in respect to which men difler more tlian in their 
powers of analysis. A Newton or a Pascal could see 



n.] METHODS OF INVESTIGATION. SECT. VI. 249 

at a glance into the relations and properties of geome- 
trical figures, what men of ordinary powers can see — 
for to understand is to see — only after hours of studj^ 
and a long process of demonstration. And to an infi- 
nite mind the result of the longest and most compli- 
cated calculation must be as evident at the first glance, 
as the first axioms of Geometry are to us. 

SECTION VI. 
Of Induction and Analogy. 

937. The words Induction, and Analogy, are each 
of them used to denote Methods of Investi- induction and 
gation, and Methods of Proof also. In one tlio&mve^fi'- 
sense of the word they are regarded as fur- nation & proof, 
nishing Predicates, in the other as proving them to be 
true. In this latter sense I shall consider them in the 
next Chapter."^ 

938. Induction f is the Method by which we colli- 

fate several facts, having identity of Formal induction. 
Voperties as a species, and in consequence of these 
facts agreeing in some other property not at first con- 
ceived as Formal, we predicate that fact of all indi- 
viduals in that species, or of the species as a whole. 

939. But when the facts of any two opposite species 
agree in any of their Formal properties (123), Analogy. 
and we aflirm a predicate of the second, on the ground 
that we had found it true of the first, we call this the 
Method of Analogy.:{: And the Method is said to be 

* Part II. Chap. HI. Sect. V. 

t Aristotle Top. Book I. Cap. XII. defines Induction to be 77 a-nh rcoi/ 
KaO' %Ka(TTov iirl ra KaQoXov €(poBos, " the way of passing from particulars 
to universals." 

J Whately has defined Analogy as being a " resemblance of ratios ; " 
and quoted Aristotle for it [^Koycov dfioiSTTj^^ But this definition does not 
seem to me either correct or sufficiently definite to answer any good pur- 
pose. We certainly speak of "facts" as analogous, as well as "ratios" 
or " relations." 

But is the analogy in the relations at all ? Is it not in all cases and 
necessarily in the facts ? Thus suppose A and B each entertain a similar 

11* 



250 LOGIC. — ^PABT n. [chap. 

that of Contraries when we aflBrm unlike or contrary 
Contraries. prcdicatcs on thc ground of contrariety of 
Formal properties. 

940. Not only do many of the facts or pbjects in 
Objects in Na- Naturc havc such properties in common, but 

F!.'rmarp?oper^ thcsc propcrtics arc taken as Formal at plea- 
^'^^- sure, and thus become matter determining a 

sphere, and the facts are subsumed under that concep- 
tion. The word " subsumed" which I have just intro- 
duced, has been pretty extensively used to denote the 
inclusion of individuals within the sphere of a con- 
ception. 

941. But no sooner do we find that we have thus 
other Proper- coustitutcd a class of iudividuals, by their 

ties common to t , . t (* ,i » 

the class be- suDsumptiou undcr any one oi their proper- 
maf ® **''' ties, than we find that there are other pro- 
perties also which are common to all the individuals of 
this class. 

942. By this fact both science and memory are 
greatly assisted. One can learn as quick, remember 
as easily and as long a general statement like this : 

. " All resinous bodies produce negative elec- 
save^timrand tricity," as hc could thc specific statements 
predicating the same thing of each kind of 
resin separately ; or even the individual statements 
predicating it of each particular piece of resin — the 
specific statements would be quite numerous, the indi- 
viduals innumerable. But the general statement occu- 
pies no more space on the written page, and requires 
no more time in enunciation and committing to me- 
mory, and no more effort to retain it, than each of the 
individual statements taken separatel3^ 

relation to C, is not the analogy between A and B ? If not, Analogy can 
answer only for illustration, and never for investigation and proof. We infer 
the relation of B to C, for instance, from (1) the known relation of A to C, 
and (2) the known analogy of B to A in that particular point which thus 
connects A to C. But if the Analogy be in the relations and not in the 
facts, the relation must be known before the Analogy ; and hence Analogy 
as a means of investigation or proof is a va-repou -n-pcoToy, a ** later-first," 
or as some might prefer to call it, a PetiHo Principii, 



n.] METHODS OF INVESTiaATION. SECT. VI. 251 

943. Hence it is of the utmost importance to science 
that such classifications should be made, and 
that in each case the generalization should ried as hilh^as 
be as high — that is, the sphere of the subject ^°^^^^^^' 
as comprehensive as th^ matter of the predicate will 
allow. 

944:. But we see objects one by one and indivi- 
dually. Nowhere are species and genera no direct per- 
objects of direct observation and intuition. p^SpiTtief ^o? 
We can never therefore find any one of the classes as such. 
contingent predicates of a class by direct intuition of 
the class-conception. We must have some other Me- 
thod of investigating their properties. 

945. We have three classes of cases coming under 
what is commonly called Induction. The Three cases. 
first is that in which we have the Formal Proper- 
ties of some class given to find the Modal Proper- 
ties common to the individuals in that class. Or 
secondly, we may have the Modal property as our start- 
ing-point, and reason from it back to the Formal ; and 
thirdly, we may have some event or phenomenon re- 
garded as an effect to find the class of objects that will 
produce that effect. 

946. (1) In the first place we fix upon the promi- 
nent and striking features which certain facts Giving a class 
have in common. We give them a general °^°^®' 
name, and have made the Properties the Essentia of a 
Genus. Then we group together other facts in the 
same way into another Genus, based upon plain and 
obvious properties as Essentia. 

947. But suppose we have a Whole to be embraced 
in our classification. Take for example the domestic 
animals of a farm. We then complete the ^e complete 
classification already begun by division, {f^^n by'^fe. 
We refer all having the properties which we ^^•^°" 

had assumed as the Essentia of horses, for instance, to 
the class " horses ; " all having the Essentia of cows to 
the class "cows;" and so on with all the classes 
which we had formed. But starting from the idea of a 



252 LOGIC. PART II. [chap. 

Whole, all the individuals in that Whole must be in- 
cluded in some one of the classes which were in the 
other process regarded as so many genera, but which 
are now in this process regarded as coordinate species. 
And if in our process of division we find any indivi- 
duals not included in any class which we had pre- 
viously constituted, we either constitute that 

Change of Pnn- , "^ . , ^ -^ i* . 

cipie of ciassi- at oucc luto a ucw Coordinate species or 

fication. T ..T fi -,, , , ^1 -i ./» 

change our principle oi division, and classiiy 
on other differentia than those with which we had 
commenced. 

948. Thus in all the Natural Sciences different 
Often done in priuciplcs of classificatiou have succeeded 

Sciences.^ '^'^^ cach othcr with every important step in ad- 
vance which the science has taken. New discoveries 
or a more careful analysis has brought to light new 
facts and new relations of fact to fact, and suggested a 
better principle of classification and nomenclature than 
was possessed before. In Botany, in Zoology, in Crys- 
talography such changes have frequently occurred. 

949. Now in this process of classification the For- 
mula used is that described above (569), in which a 

Formula of commou predicate denoting the Essentia of 
Classification, ^j^^ Gcuus is affirmed of the individuals com- 
prehended under it individually. When this has been 
done we give to the individuals a class-name, and then 
the matter of this class-conception gives the limits to 
its sphere, by including in it not only the colligated 
individuals which had been named in the process of 
the classification, but also all others which have the 
Essentia of the colligated individuals, and which con- 
stitutes the matter of the class-conception. 

950. We now come to the next step in the Induc- 
common Mo- tiou. Wc find that scvcral individuals in 

p^edicated^"^ *^^ the gcuus tlius formcd have a Modal pro- 
perty common to them all, which however was not so 
obvious as the property upon which our classification 
was based, or which at all events was not included in 
our class-conception. We then predicate this property 



n.] METHODS OF INYESTIGATION. SECT. VI. 253 

of the individuals in the class, one after another as 
above (571), and then predicate this property of the 
class as a whole. And this deductive judgment aflfirms 
the Modal property of the species as in the example 
given (570). 

The wolf is carnivorous ; 

The fox is carnivorous ; 

The cat is carnivorous, &c. : 
.-. The Canidw are carnivorous. 

951. And when we have thus affirmed a property of a 
whole class we speak of it as a law of JSTature. General Facts. 
It is in truth, however, but a general fact, and wants 
much yet of being what can properly be called a law.^ 

952. There are three steps in Inductions of this class 
which it will be well to notice separately; Three steps of 
not indeed as involving or depending upon induction, 
diiferent principles, but as being different and wider 
applications of the same principle. 

953. {a) For the first let us take the following : 
We learn of an individual animal a property which 

was not included in its class- conception, as First step, 
of the horse, the fact that he sheds his hair every spring. 
We soon learn of the next horse that we become ac- 
quainted with, that he also sheds his hair in the same 
way. After learning this fact of a number of indi- 
viduals in the species horse, we predicate the fact as a 
general fact or law with regard to the species, that 
" horses shed their hair every spring." 

954. This may be regarded as illustrating the first 
and primary step in Induction. It is a pro- T^jg process 
cess which we all go through with in refer- aJqSin'' ^of 
ence to many of the most common species knowledge, 
of facts, long before we reflect upon the process at all, 
or study its laws. 

955. (5) Then for the second step take the case in 
which we extend or widen our induction by r^^^ second 
including several species. Thus, ®*^p- 

* See Part 11. Chap. m. Sec. V. 



254 LOGIC. — PAET n. [chap. 

The cat has canine teeth ; 

The dog has canine teeth ; 

The wolf has canine teeth ; 
therefore the dog, and the wolf, the cat and all animals 
which have canine teeth constitute a natural genus, 
which we will call the Canidce. 

But the dog is carnivorous ; 

The cat is carnivorous ; 

The wolf is carnivorous ; 
therefore the Canidae, or all animals with canine teeth, 
are carnivorous. 

956. {c) For the third step we take the fact or law 
Third step. thus dcvcloped as a Formal property, and 
constitute upon it a species of '' Carnivorous Animals ; " 
and in the course of our investigation we find that their 
habit of life is always accompanied by a peculiarity of 
the digestive organs and alimentary canal, the stomach 
being smaller and the canal much shorter than in 
herbivorous animals. We have now established an- 
other fact. We may make this fact a Formal property 
and proceed with our investigation as before, showing 
that all animals with this kind of digestive apparatus 
possess more energy and activity, and stand higher in 
the scale of being, if we will measure their rank by 
the power of control. Thus the lion and the tiger, 
though much smaller, control the elephant, camel, &c. 

957. (2) If now our investigations had began at the 
The second Other cud, if we had seen the animal eatins: 

class : cases m ^ i i i ±^^ i_ ^ • 

which we begin ilesn, and SO known that he was carnivorous 

with the Modal ir» ijj* jii t'j. f» 

Properties. Deiorc wc had discovered the peculiarity oi 
his teeth, we should have regarded this Mode as some 
indication of what could be found in the constitution — 
that is, among the Formal properties of the animal. 
It would then become a case for the investigation of a 
Formal property indicative of this Mode of life ; the 
Method then becomes the same as that for finding the 
Cause when we have an eflect given. "^ Canine teeth, 

* See the next Section. 



II.] METHODS OF INVESTIGATION. SECT. VI. 255 

however, cannot be regarded as a Cause, notwithstand- 
ing they may be the Sign, of that mode of life. 

958. Having by this Method ascended from the 
Modal to the Formal property, we reverse Having found 
the order and predicate the Mode of the spe- pen^' wl^ ^fe- 
cies upon the ground of the Formal property ""^'^^ ^^® **''^^'^- 
which is its sign, just as when the Formal property had 
been our starting-point in the order of time. 

959. (3) There are cases in which we have a pheno- 
menon occurring, which we regard not as a ^hird class : 
Modal property, but merely as an occasional ocSonai''^ef- 
effect. For an example take the case of ^^''^^• 
electricity excited by resinous bodies. The appear- 
ance of the electricity is not a mode of the resinous 
bodies, it is merely an effect of their excitement by 
silken or woollen surfaces. 

960. In this class of cases the Induction is scarcely 
any thing more than a classification with a induction in 
view to the general fact. We find one kind ^'^l^'ceiy ""any 
of resins, shellac for example, susceptible of I^^^^l ciaS 
negative electricity. But we cannot find in *'^*^®^' 

our analysis of shellac any thing which seems to us 
likely to cause electricity, any thing by which we can 
predict a priori on finding the same property in sub- 
stances of another kind that they will excite the same 
kind of electricity. We soon find, however, that other 
resins do excite negative electricity, and thus far in our 
experience all known resins agree in this peculiarity. 
But why, or what is the property in them by which 
they produce an effect so unlike other substances under 
the same circumstances we cannot tell. Chemistry 
reveals to us many such cases, and it is quite possible 
that they point to something yet to be discovered, but 
which is at present beyond even the forerunning con- 
jectures and hypotheses of science. 

961. And yet when the nature of electricity is bet- 
ter understood we may be able to see some- Further know- 
thing in resins — some element common to ven%h;^m S 
them all as a constitutive or Formal principle d3ins! ^°" 



256 Loaic. — TART n. [chap. 

of the class, whicli we shall then understand to be as 
naturally adapted to the production of that particular 
state of electric excitement which we call Negative 
Electricity, as the canine teeth of the Oanidse are to the 
carnivorous habit of life. The Analogies of Nature 
and the developments and progress in. the history of 
Science lead us to expect such a result. 

962. But as it is, we place much less dependence 
upon the inductions of this class than upon those of 

These ciassi- clthcr of thc othcrs. We regard them in 
festive ' of ^ if feet as but mcrc classifications of particular 
ductions. facts into a General fact, preparatory to an 

induction and prophetic of it, which, however, we are 
not fully prepared to make. 

963. In the course of our induction we for the most 

Exceptions be- part flud somc exceptions to the general fact 

S'"1ead^°°to which we first deduce in this way. And so 
new assi ca- g|.j,Qjjg|y ^j.^ ^q attachcd to thc fundamental 

ideas under which we pursue any science, that when 
the exceptions become very numerous we abandon the 
classification upon which the induction was based, and 
classify anew and on another principle. Thus the old 
philosophers predicated the property of ^^ falling " of 
heavy bodies only, such as earth, stones, metals ; and 
they supposed that light bodies, as air, vapor, and 
smoke belonged to an opposite class, of which " as- 
cending " could be predicated by the Method of Con- 
traries. But it has been found that light bodies also 
tend to the earth, and now a new classification has 
been made, and " falling " is a property predicated of 
all bodies having the common Essentia of being " un- 
supported." And we state it as a general fact, that 
" all bodies left unsupported fall to the earth." 

964. We have already remarked that those proper- 
Natural ciassi- ties upon which the classification of natural 

fications not of- •"■ ^ -, , n , i 

ten based upon p-eueras arc based, are not sreneraliy those 

variable proper- ^ ^ > ^ i • ^ ^ • x* • ^ 

ties. which are subject to comparisons ot inten- 

sity, as color^ size^ density^ &c., among material pro- 
perties ; virtue, wisdom, courage, &c., among spiritual 



n.] METHODS OF INVESTIGATION. — SECT. VI. 257 

properties, but rather those which do not admit of any 
such comparison. In the case just given, bodies either 
are or are not supported. If one is supported, it re- 
mains where it is, if not, it falls. We take no notice 
of the fact of the support being adequate to sustain a 
body many times as large ; that fact has no bearing 
upon the classification or the deduction based upon it. 
JNTor if there be something under it which is not suffi- 
cient to support it, do we take notice of that fact — the 
body is simply " unsupported." 

965. But in the previous classification in which it 
was affirmed, that " all heavy bodies fall," the classifi- 
cation was based upon a property which admits of 
comparisons of intensity. Bodies are more or less 
heavy. " JSeavy^^ and " light ^^ are not, like " sup- 
jported^^ and '^ unstcpportedy^^ contraries, but they are 
simply sub-contraries / and the Induction based upon 
that classification was fallacious. It stated the truth, 
indeed, but not the whole truth ; and the suppressio 
veri was for all purposes of science just as bad as a 
false statement. 

966. Analogy stops short of an Induction of the 
second degree (955), because for the most 

part the objects of the class to which the an Tncompiete 
inference is drawn — that is, the subject of 
the Conclusion is beyond the reach of actual Observa- 
tion and Experiment. But if we could investigate the 
individual to which we reason by analogy, we should 
convert such Analogy into an Induction of observed 
facts in the same species. 

967. In all the Inductive Sciences there are many 
of the fields of inquiry from which by the 

nature of the case we are excluded, and extenVto^ fields 
there are others which neither our telescopes ^infnSM^ ^S 

1 T T impracticable. 

nor our microscopes can reach. In such 
cases Analogy is our only guide and furnishes our only 
light — a light indeed of inestimable value, but still a 
light which needs to be most cautiously followed. In 
the anatomy of the human frame, for instance, we have 



258 LOGIC. — ^PAET n. [chap. 

the facts for an induction before us. But in physiology 
and biology many of the facts are such that they never 
can be brought under inspection and observation. 
Comparative Anatomy, however, has shown an analogy 
between man and animals ; and we may often subject 
them to an examination into the functions of reproduc- 
tion, life and death, which we can never make in the 
case of man. 

968. All substances are brought by their Formal 
The Formal propcrtlcs luto rclatiou to the laws and 

spe?feV^^ bring scQuences of nature. Thus bodies that are 

them within the . ^ . i ii • j , i 

field of Analogy, transparent, are by tms property connected 
with an important class of phenomena and laws in 
optics. Resinous bodies, by a property common to 
them all, but which has no distinctive name, are con- 
nected with the science of electricity in one way ; and 
vitreous bodies, by a property common to them, are 
connected with the other kind of electricity. Iron by 
a peculiar property is capable of important magnetic 
phenomena, and the laws of terrestrial polarity. 
Dense bodies, by their density, are connected with the 
laws of gravitation. Opaque bodies, by their opacity, 
with reflection of light and the phenomena of color. 
Thus every Formal property of a body connects it with 
some general law or fact — some class of phenomena 
more or less comprehensive ; and those relations are 
the basis of the natural genera and species upon which 
all science and all knowledge depends. 

969. Each property of a body is thus connected in 
the concatenation of nature's laws and sequences, with 
some law and with some phenomenon, which as a con- 
sequent is regarded as an effect or a mode. 

970. Now when in such a natural species we find 
one property which is regarded as Formal, connected 

ApDiication of witli a ccrtaiu law and producing certain 
Analogy. effects, we infer by analogy that any indi- 

vidual in another species, having the same Formal 
property, must sustain a like relation to that law, and 
have the same modal property or effect. 



n.] METHODS OF DSTYESTIGATION. SECT. VII. 259 

971. Thus the physician knows that a certain drug 
is a deadly poison to some of the animal tribes. He 
infers from analogy between the animal and By the Medical 
man that it will prove so to man. He knows practitioner. 
that there are many points of identity between man 
and the animals — they have an Essentia in common ; 
he knows that most drugs produce the same effects 
upon men as upon animals. But with regard to this 
particular drug's influence upon man, or whether man 
and beast are identical in that particular property, in 
consequence of which that drug is a deadly poison for 
the beast — he knows nothing anterior to experience of 
its effect upon man except what he can infer from the 
analogy between the man and the beast. 

SECTION VII. 
Of Elimination, 

972. The facts of Nature have not only a lateral 
connection, so to speak, by which they admit 

of classification into Genera and Species, Natu?e h\ve re" 

.,1 . , iy»i. Ill/ lation of ante- 

with a View to general lacts and laws, but cedent and con- 
each one had something before it which is ^^'^''^"^' 
regarded as its Cause, and will be followed by some- 
thing which will be regarded as its Effect. 

973. Causality is not a property inhering in any 
substance that can be cognized by any of the causality not 
senses. We can see antecedence in time, Jemfbir^in^lt- 
but the causality is a matter of inference. ^^^^• 

974. Causality^ however, is something more than 
Inere antecedence and necessary connec- causality some- 
tion.^ Day and night follow each other, Jhing more than 
the successive steps of the pedestrian, the ^^°^^- 



antece- 



* The Fallacy which we sometimes hear spoken of as the Fallacy of 
;post hoc ergo propter hoc^ consists in inferring that because one event is after 
another, therefore it was caused by that other. Bishop Latimer exposes 
this fallacy in some who attributed the laxity of morals in his time to the 
Reformation, by narrating the anecdote of a countryman who accounted 



260 LOGIC. — ^PAKT II. [chap. 

days of the week, the months of the year, all succeed 
each other, and yet no one supposes that each is the 
Effect of that which preceded or the Cause of that 
which follows. So the antecedence is a fact in the 
reality of being ; the causality, where there is any, 
belongs to the reality of truth alone. It seems to direct 
the thought into the unseen realities of truth ; and the 
Reason, by an intuition peculiar to itself, sees there 
what is not expressed in the sensible properties of ex- 
ternal objects. 

975. By means of Induction we may always find 
the Invariable Antecedent in the phenomena of Nature. 
Invariable An- But thc distiuctiou betwccn a mere Antece- 
btiffl'^'by^ln" d^nt ^^d a Cause, is what no processes of a 
duction. posteriori investigation can give. It is some- 
thing which the Reason superadds to the results of our 
investigation in certain cases, just as in Induction the 
Reason superadds that which distinguishes a General 
Law from a mere General Fact. By the insight which 
Induction enables us to get into the Class-conceptions 
and Final Causes of the Creator, we are enabled to 
aflirm the concomitance of certain properties of objects 
as Laws arising fi^om that physical necessity which is 
based upon the volitions of the Divine Will. So, too, 
by Induction we establish certain antecedences and 
consequences in Nature as general facts, upon which 
the Reason infers or rather superadds the relation of 
Cause and Effect. 

976. All investigation of Causes must of course end 
The Causes in at last in thc Absolute or First Cause (108). 

condaiy. But tlic Mcthod whicli we are now describ- 

ing must proceed step by step, and from any one fact 
or event it can give us only that which next preceded 
it in the order of time and of causality. This becomes 

for the sands that obstructed the Goodwin Harbor — by the building of Ten- 
terden Steeple — " There were no sands," said he, " in the harbor ; that is, 
none that gave trouble, until just after the steeple was built on Tenterden 
Church." Hence the good people of Tenterden supposed that the steeple 
had caused the sands in their harbor. 



n.] METHODS OF INYESTiaATION. SJICT. VH. 261 

in its turn an Eflfect to be investigated in like manner, 
until in like manner " omnia exeunt in Deum " (all 
things lead to God). Then and then only do we find 
an Efficient Cause for the facts and phenomena of 
Nature. 

977. This results from the fact that Matter is always 
regarded as inert, and incapable of acting ^^^ ^^^^^^, 
except as it is acted upon. Even the im- °^^"^^- 
ponderable agents, heat, light, electricity, &c., can 
hardly be regarded as exceptions to this rule. As yet 
we know not what they are. But the Reason refuses 
to regard them as any thing more than means, Instru- 
mental or Second Causes in the hands of an Intelligent 
or First Cause. 

978. Our inquiry into Causes therefore can be only 
an investigation into the antecedents of any 

event, along which the mind conceives that ditions rlqui?e"d 
the efficiency which brought that event into 
the reality of being may have passed. And the only 
conditions which the Reason imposes are, (1) that that 
which is to be regarded as a cause be an invariable 
antecedent ; (2) that it be a true cause ; and (3) that it 
be a sufficient cause {causa vera and causa suffi- 
ciens']. 

979. Of the first we need say no more than the self- 
evident proposition, that a cause must pre- First lAntece- 
cede its effect in point of chronology. denceinTime. 

980. Of the second, we can only say that a true 
cause must be a substance acting through second: a sub- 
some of its properties. A mere state or mode ^^"''^• 

of a substance is no cause, although of course it will 
often be an antecedent. Thus " day " is a mere mode of 
light, and is no cause of the succeeding mode ^ Mode no 
which we call " night." One of the steps of a p^'^p^' ^^"'^• 
pedestrian is merely one condition or stage in his pro- 
gress, and no cause of the succeeding one. " Day " 
and " step " are not substances in the metaphysical 
sense of the words at all (Part I. 55 and note), but 
merely modes or stages of certain substances. Thus 



262 , LOGIC. — ^PAET n. [chap. 

the step that crushes the worm cannot be regarded as 
the cause of the crushing. Not the step but the man 
who steps is the cause ; and the word " step " denotes 
Substantive & Hierely the accidental condition or mode in 
Modal Causes, ^^ich thc causc happened to be when it 
exerted its efficiency. It may be well, therefore, for 
the sake of having a name, to call the former the Sub- 
stantial or Substantive Causes, and the latter the Modal 
Causes. 

981. But not only must the antecedent which we 
are to regard as a cause be a substance, in order to be 

Cause must ^ "^^"^^^ causa^ it must also bear some propor- 
^rtion"^fo^its tion or relation to the effect in order to be a 
Effect. sufficient cause, or causa siifficiens. Thus, 

a boil on one's hand may be a vera causa of a good 
deal of pain and annoyance, but it would not be re- 
garded as a sufficient cause of the death of an indi- 
vidual, if one having such a sore should be found 
dead. 

982. The substantiality^ (38) of causes must be af- 
firmed by an ultimate intuition of the Mind itself. One 

The substan- ^au uo morc prove that a " day " is no sub- 
uftimate^'intui? stautlal causc than that the sun is round, or 
tion. ^ pQgg jg Pg(j^ jf Q^p faculties do not so see 

these objects, there is no help for us in one case any 
more than in the other. The fault is an individual in- 
firmity, and can be regarded as requiring no diminu- 
tion of the confidence which all persons whose faculties 
are in their normal condition are entitled to place in 
the exercise of those faculties. 

983. But the sufficiency of causes in Nature is what 
The sufficiency wc cau Icam ouly fi'om observation. Of 
Jfaturniarned Primary Causcs, as of the Infinite Mind, and 
ti^™and^'nduc- ^^ ^^^ humau miud, from the very conception 
tion. Qf them we can predicate certain events or 
phenomena as eflects. We know that Infinite Wisdom 

* When we speak of a cause as being necessarily a substance, we must 
be understood as speaking not of mere antecedence, but of causality. An 
antecedent need not be a substance, but a cause must. 



n.] METHODS OF INVESTIGATION. SECT. VH. 263 

will know all things — Infinite Power can do all things, 
that Mind or Eeason can understand, that Will can 
choose, and determine the formal character of actions. 
And so in Nature we may predicate a priori^ on the class- 
conception of certain objects something of their conca- 
tenation in the antecedents and consequences of Nature. 
But this class-conception is itself obtained a posteriori^ 
and the nature and efficiency of their causality is a 
part of that which we learn by observation, and through 
which we are enabled to arrive at this class-conception. 
It is certainly very possible, and perhaps we had bet- 
ter say that it is probable, that the causality of all 
objects was an element in the class-conception which 
preceded in the Divine Mind the act of their creation. 

984. In the sufficiency of causes we have two dis- 
tinct elements to take note of — the adequacy . 

in amount and homogeneity in kind. Thus cause^iSdes 

,1 f¥?' , {* * X • ,* two Elements. 

Wine IS the suincient cause oi intoxication. 
But a single wine-glassful would be inadequate in 
quantity. But if one should attribute a scarlet fever 
or the small-pox to the use of wine, he would mistake 
the homogeneity of the cause to the effect which he 
ascribes to it. Wine is a cause, a vera causa^ and a 
causa sufficiens of a variety of phenomena, but not of 
the diseases just named. 

985. As every cause must be a substance, and every 
substance is known only by its properties, so also it is 
known only as existing in some certain con- causality often 
dition or mode ; and this condition or mode S^Jmode of the 
is often inseparable from that antecedence substance. 

to the effect which renders the substance a cause of it. 
Thus wine is a cause of intoxication only when taken 
into the stomach and in a certain quantity. The Air 
is a cause, but it causes the uprooting of trees, and the 
other effects of tornadoes only when it exists in the 
mode of violent motion. 

986. Hence we have four classes of words Four classes 

T . T T i 1 i ot words used 

or terms which are used to denote causes : — to denote cau- 
(1) Simple words denoting substances, as 



264 LOGIC. — ^PART n. [chap. 

" heat," " electricity," " light," &c., substances whose 
efficiency as causes is always active wherever the sub- 
stances themselves are found ; then (2) we have such 
words as denote merely the condition or mode in which 
the cause exerts its influence, as when we say that 
" walking fatigues one," — " the succession of day and 
night causes great changes in the temperature," &c. 
Then we have (3) those complex terms which express 
both the cause and the mode or condition upon which 
the production of the effect depends, as " the spakk 
falling upon gunpowder caused the explosion." Or 
sometimes (4) we have single words which in them- 
selves express the substance and its modes, as " earth- 
quake," " hurricane," " lightning," &c. 

987. Words or terms in order to express a cause 
adequately should always be of this last-named kind. 

The last kind They should cxprcss not only the substance 
^aisladequat'e^- which is the causc, but also the mode or 
^^' condition on which the efficiency as cause 

is exerted. 

988. The immediate Antecedent of any phenomena 
Simple and wiU somctimcs be complex, consisting of 

ceTSts?" ^'^^^' several elements, and at others simple. Thus 
Heat is a simple antecedent. It admits of no phy- 
sical analysis. But the sun — a burning lamp — acidi- 
fying vegetable matter — the mixing of sulphuric and 
nitric acids — are all complex antecedents, compound- 
ed of the simple antecedent or cause, heat, among 
others. 

989. We must remember also that in regard to 
many of the compound facts in Nature, as elsewhere, 

The Causality ^hc causality is not to be found in any one 
Spon the^^com- ^f ^hc ingrcdicnts or elements alone and by 
ptexity. itself Thus, it is not the charcoal, nor the 

nitre, nor the sulphur which causes the explosion when 
a spark falls upon that combination of these three ele- 
ments which constitute what is called gunpowder. 
Neither of those elements are explosive alone and by 



n.] METHODS OF INVESTIGATION. SECT. VH. 265 

itself.*^ Not any property of either of the substances, 
therefore, is the cause of the explosion — the combina- 
tion itself is the cause. 

990. When therefore the combination is the cause, 
and not any one of the simple elements in that combina- 
tion, the complex antecedent is to be regarded ^o Eiimina- 
as the cause. But it is often the case that ^Xn^heTa'If- 
some one element in the complex antecedent l^^^y thl'^com^ 
may be the cause, and it will in many cases p^^^^^^^- 

be found of the greatest importance to ascertain which 
of the simple elements in any complex antecedent is 
the real cause of the phenomena which we are investi- 
gating. 

991. For this purpose several Methods have been 
resorted to, which have been called Methods Elimination. 
of Eli7)iination. They consist in removing entirely or 
varying in quantity certain of the elements in any 
complex antecedent or consequent for the purpose of 
ascertaining its relation to the supposed Consequent or 
Antecedent. 

992. Elimination depends upon the four following 
axioms : 

(1.) No two simple causes will produce the same 
effect and the converse. Hence identity of First Axiom. 
effect implies identity of cause, and diversity of effect 
implies diversity of cause. 

993. Several complex antecedents may be followed 
by the same effect. Thus a wax-taper, an oil-lamp, a 
coal-fire, the concentrated rays of the sun, may each 
be the cause of the melting of sealing-wax. But in 
these comple:?c antecedents, there is identity in one sim- 
ple element " heat," by which the eftect is produced. 

994. And so strong is the belief in this axiom of 
identity of cause, where there is identity of effect, 

* This has recently been disputed in regard to Nitre. But I believe 
that its explosiveness has not been proved. But even if it has it will not 
affect the propriety of the illustration ; since if it is explosive at all, it is 
not explosive under any such circumstances as those contemplated in the 
text 

12 



266 Loaic. — ^PART n. [chap. 

that scientific men cling to it even when facts seem to 
Influence of he against them, and the belief in its infalli- 
the ''minds'^of bilitj has often led by means of an analysis 
°^®^- of the complex antecedent to the discovery 

of what would otherwise, perhaps, never have been 
suspected to exist. And in investigations of the phe- 
nomena of Electricity, Galvanism, and Magnetism, the 
identity of effects produced in many cases have led 
very generally to the belief that these forces are but 
one and the same thing, acting in different ways and 
under different circumstances. Nay, so far has this 
matter gone, that it has been suggested that this one 
cause " Electricity," if that be the name of it, is the 
cause of heat and light, and the medium through which 
the mind exerts its control over the body. 

995. As we know nothing a j^^osteriori of substances 
except through their properties, so we know nothing 

Axiom proved ^^ causcs as causGS — that is, nothing of the 
a priori. causality of objects in Nature, except by 

inference from their effects. As we have already said, 
a cause must be a substance, it must be adequate and 
homogeneous to its effect. And as the identity of ob- 
jects in Nature depends upon the identity of their 
inseparable properties, so the identity of causes as 
such must depend upon that which constitutes their 
adequacy and homogeneity to the effect produced. 
Hence the proposition already laid down, " the identity 
of effect implies identity of simple cause." 

996. (2.) The second axiom is, that if the cause is 
Second Axiom, rcmovcd the effect wdll disappear. Other- 
wise we should have an effect without a cause, which 
is absurd. 

997. (3.) The magnitude of the effect varies with 
Third Axiom, and is determined by the magnitude or in- 
tensity of the cause. Otherwise we should have some 
portion of causation without any effect, or some por- 
tion of effect without a cause. 

998. (4.) And fourthly, that codevis paribus the same 
rourth Axiom, c^use wiU always produce the same effect. 



n.] METHODS OF INYESTIGATION. — SECT. VII. 267 

999. The effect always depends very mucli upon 
the substance or matter upon which the cause exerts 
its force. Thus heat expands iron, and con- Efficiency de- 
tracts clay ; and as has been said, " what is sSSjict'matter! 
one man's meat is another's poison." 

1000. This leads us to mention the fact that Con- 
sequents as well as Antecedents are complex consequents ai- 
also, and as such the result of more than I2npfe™^ 
one simple cause. Thus, for example, an eclipse of the 
Moon, considered in its essence as an eclipse, and in 
its modes as occurring on such a moment and visible 
only at such a place on the Earth's surface, is a com- 
plex result, caused by the various forces of the diverse 
attractions of the different heavenly bodies. In this 
case the cause of the eclipse was one thing, the cause 
of its occurring at precisely that moment rather than 
another, or so as to be visible on one part of the Earth's 
surface rather than another, are each of them different 
causes, and may be called Formal Causes. In this case, 
however, we use the name Formal Cause in a sense 
somewhat different from what we have given to it in 
reference to logical classifications, and yet not so dif- 
ferent as to occasion any confusion -or error. 

1001. Let us now proceed to consider the several 
Methods of Elimination. Of these we may Five Methods 
have five that are specially useful, arising «>f Elimination, 
out of the axioms already mentioned as applied to the 
different cases which may arise for investigation. 

1002. The first law of Elimination in the order in 
which I shall name them is the following : 

(1.) By the Elimination of any one element in the 
complex antecedent^ its apjprojpriate conse- First Method. 
quent or effect will disajopear also. 

1003. Thus suppose a physician administers a pre- 
scription consisting of three ingredients, camphor, and 
morphine, and ipecac — and finds unpleasant lUustration. 
symptoms ensue that can be ascribed to nothing but 
the dose which he had prescribed. Suppose now that 
he administers two of the ingredients without the third, 



268 LOGIC. — ^PAET n. [chap. 

or the two combined with some others, and the un- 
favorable symptoms do not ensue, he would doubtless 
ascribe those symptoms as an effect to that ingredient 
in the dose which in the second administration he had 
omitted. 

1004. (2.) When there is a uniform disagreement 
Second Method, in severol Antecedents in all the elements 
except one^ that one must he regarded as the cause of 
any unvarying element in the Consequents of those di- 
verse Antecedents. 

1005. Thus suppose we have an Antecedent A, 
Illustration. cousistiug of elcmcnts x^ y^ and ^, and a 
Consequent C. If now we can form or avail ourselves 
of new combinations 2i,^ w x and v^ or s x and t^ having 
X alone common to them all, and the Consequent C 
following in each case, we should have no doubt that 
A is the cause of C, by reason of its element x. 

1006. Such cases occur not unfrequently in Chem- 
ofuseinchem- istry, whcu wc havc to deal with asrents 

istry and Phar- i • i .ii i . • ^ , 

macy. which wc cithcr cannot get m a separate 

and pure state, or if we could their use would be in- 
convenient or unsafe. The same thing holds true also 
in Medical practice*. Some of the most indispensable 
of the medical agents, in fact nearly all of those that 
are the most efficient can never be used except in 
combination with others. Hence their effect can be 
ascertained only by forming them into different com- 
binations, varying in each experiment every other 
ingredient. 

1007. (3.) JBy diminishing or increasing the cause^ 
Third Method, a corvcsj^onding increase or diminution of the 
effect will ensue, 

1008. This law of Elimination supposes a case in 
which the element in the compound Antecedent cannot 
be wholly eliminated. 

1009. Thus " heat " is an agent of this kind. There 
iiiu3tration. is uo absolutc of cold or total absence of 
heat. But we can increase or diminish the intensity 
of heat to a very great extent. Thus we find that 



n.] METHODS OF INYESTIGATION. SECT. VH. 269 

nearly all bodies expand — become liquid, and finally 
vapor, and even gas, under intense heat ; and in the 
absence of heat all bodies contract, condense, and be- 
come solid. Hence heat is assumed to be the cause of 
fluidity. The same may be said of density. There is 
no body without some density ; and as the gravitation 
of bodies, so far as we can ascertain, varies with their 
density — we assume that density is the cause of the 
gravitation of bodies, or that all bodies gravitate in 
proportion to the quantity of matter. 

1010. (4.) If ^ from any pair ^ consisting of a complex 
Antecedent and a complex Consequent^ we FounhMetnod. 
separate the elements in the Antecedent^ whose effects in 
the complex Consequent are Tcnown^ and find an element 
in the Consequent whose cause is not contained in the 
Antecedent^ it is called a Residual Phenomenon, for 
which a cause must ie sought. 

1011. We have many cases in which the several 
elements of a complex Antecedent have been Residual phe- 
so far examined, as that their efiects both in "o^^ena. 
quality and quantity in the Consequent are known, 
and yet something remains to be accounted for. The 
return of a Comet may be regarded as such ^ t^e return 
an effect. Now among the causes which comets, 
determine its return we know many — the attraction of 
the Earth, the attraction of the Sun, and of each of the 
other heavenly bodies to which it approaches in its 
path near enough to be influenced by them. These 
different attractions are the elements in the cause of 
its return, considered as a complex Consequent, in- 
cluding its return at a precise day and hour, &c. If 
now we begin and abstract from the Cause each ele- 
ment, deducting from the Consequent also its appro- 
priate effect — appropriate both in character and in 
amount, in quality and quantity, and after thus ab- 
stracting each element in the Cause with its element in 
the effect, we find something remaining in the effect 
still unaccounted for — we have what Sir John F. W. 
Herschel called a Besidual Phenomenon. Thus if we 



270 LOGIC. — ^PAET n. [chap. 

have Antecedent compound oi a^ 5, c^ and d ; and Con- 
sequent consisting oiw^ x^ y, ^, and s ; and abstracting 
a from the Antecedent removes w^ h removes x ; c^y / 
and d^ z. We have s remaining as a Residual Pheno- 
menon, for which a cause is yet to be sought, and to 
be added to our enumeration of the elements a^ J, c^ 
and d in the Antecedent. For the elements in any 
Cause must be adequate to the Effect, and the v^hole 
of it both in Substance and in Form. 

1012. The existence of a resisting medium filling 
all space, and yet so rare as not to exert any perceptible 

influence upon the motions of the planets 

The existence -y iit. r« i i ^ 

of a resisting auQ Satellites 01 our system, has been sup- 
Medium proved Til 1 T 1 -n»»Ti 

as a Residual poscQ to uavc Dcen Giscovered as a Kesiduai 
Phenomenon, effected by means of this Me- 
thod in accounting for the return of comets at a period 
somewhat less than that assigned them by the calcula- 
tions of astronomers. But whether there be such a 
medium or not, the Residual Phenomenon shows that 
there is some agency at work of which as yet we pos- 
sess no satisfactory knowledge, and which will need to 
be investigated before the science of Astronomy will 
be complete. 

1013. (5.) Again and finally, there may sometimes 
a doubt arise as to which of the two phenomena are 

Necessity for a ^^ ^c regarded as cause and which as effect. 
Fifth Method. Thus, it is always observed in cases of snow- 
storms, that just as the snow begins to fall the mercury 
in the thermometer rises a little. Now, is the change 
in the temperature the cause or the effect of its begin- 
ning to snow ? In thunder-storms, a flash of lightning 
is sometimes attended by an increase in the quantity 
of rain that is falling ; which is cause and which is 
effect ? 

1014. In many of these cases we can answer from 
The doubt set- our knowlcdgc of the nature of the pheno- 
c^ses b"y r^t mena themselves. And there are many 

wi knowledge . , . , i • ^ 

of Causes. cascs lu wliich wc cau make no experiments 
of Elimination. But when elimination can be made, 



n.] METHODS OF mVESTIGATION. SECT. VU. 271 

the case comes under the second axiom. Hence we 
have as the fifth rule of Elimination, 

1015. (5.) Remove one of the phenomena^ and if the 
other disappears also^ that which was re- Fiiih Method. 
moved is the cause and the other is the effect. But if 
the other does not disappear^ that which was removed 
was the effect and not the cause, 

1016. For an illustration of this law it is very com- 
mon to refer to the case of Dr. Wells' researches into 
the phenomena of dew. It was found in the illustration. 
course of his experiments that those surfaces on which 
dew collected, were colder than those upon which there 
was none. But which was the cause and which the 
effect, the cold or the dew? By substituting metal 
surfaces, which do not easily become cold in the posi- 
tion in which he placed them, for glass, which being a 
bad conductor does easily become cold, he found that 
the glass surfaces and not the metal were covered with 
dew, whence he inferred that the cooling of the surface 
was the cause of the dew, and not the dew the cause 
of the cooling of the bedewed surface. 

1017. Having in these ways learned the nature of 
objects considered as causes, we can often Reasoning from 

•^ • i • J • i j^i j^ i r» known causes 

reason or mvestigate into the luture irom into the future. 
causes- to their yet undeveloped effects."^ Eeasoning 
in this Method, however, is jalways attended with some- 
thing of danger. We seldom thoroughly comprehend 
all the properties of a Cause, or the influences which 
may be exerted upon its efficiency by its combination 
with other causes. Nor can we ever see far enough 
into the future to enable us to take into our account all 
of the contingencies that may arise to modify the com^se 
of events. Thus we can predict the fall of an unsup- 
ported body from our knowledge of the law of gravita- 
tion. But another law, as magnetism or electricity, &c., 

* TMs has also been called " reascming ajpriori" — Whately's Rhetoric, 
Part I. c. II. 32. It is not, however, a priori in the sense in which wo 
Have thus far used these words. 



272 LOGIC. — PART n. [chap. 

may interpose between the cause and the effect and 
break the connection. 

1018. But yet there are many cases in which this 
Sometimes our is thc ouly Mcthod by which we can pene- 
fo"re^ca?t?ifrthe tratc thc futurc. The astronomer reasons 
VAstronomy. upou it iu predicting the rise and set of the 
sun, the changes of the moon, the recurrence of eclipses, 
comets, conjunction of the stars, &c., &c. And he feels 
perfect confidence in his conclusions. 

1019. The chemist reasons in this Method when he 
In Chemistry, dcsigus au experiment. He knows the ef- 
fects which certain agents as causes generally produce. 
He reasons from this knowledge to the effect which 
those agents will produce in the new case, and trusts 
to this calculation to produce the test or crisis which 
he wishes to determine by his experiment. 

1020. The physician reasons on this principle when 
In Medicine, hc prcscribcs his remedies, and looks for the 
desired change in the condition of the patients as the 
effect of what he had prescribed. 

1021. The legislator has to rely on this Method in 
In Legislation, thc discharge of his duties, as legislator, to a 
very great extent. It is often his only guide in devis- 
ing laws and institutions for the welfare of those for 
whom he is called upon to legislate. And the causes 
whose influence he has to calculate, are moreover often 
of the subtlest and most evanescent or incomprehensi- 
ble character. 

1022. It will have been observed from the fore- 
Reasoning from p:oin2; remarks — that in speakinar of the cause 

Effect to Cause ^^ r i. j. n . ^ j 

limited. 01 any lact or event, we reier to a compound 

object within which one element alone was caused of 
the eitect. Hence reasoning from effect to cause, we 
can reason only to that element, and not to any one 
of the combinations into which it may enter. Thus 
heat is the cause of fluidity. If now we start from 
fluidity, as an effect, we can argue to the existence of 
heat as a cause. But as this heat may have been pro- 
duced by the sun, by a spirit-lamp, by a chemical 



II.] METHODS OF INYESTIGATION. — SECT. VH. 273 

decomposition, by friction, (fee, (fee, we cannot argue 
to the reality of any one of those combinations of heat 
from the mere fact of fluidity. Hence we can investi- 
gate and argue much more specifically from cause to 
effect than Irom effect to cause. 

1023. In some of the most important inquiries 
which we can have to make, however, we Limited in 
have no other Method that we can pursue, S^lsomng^roS 
but that from effect to cause. In Medical Effect to cause. 
diagnosis, for instance, this is for the most part the 
only means of ascertaining the nature of the disease to 
be cured. 

1024. The physician is called to see a patient — the 
prominent symptom is we will suppose a illustration. 
headache — this is an effect which may proceed from a 
variety of causes. If it were the first case of headache, 
and had never been investrgated, there would be no 
other Method that could be pursued with success than 
those we have already described. But in the present 
state of the science almost all causes, and varieties of 
causes, have been investigated. The causes which 
may produce such results are pretty well known and 
recorded. 

1025. Each cause also, for the most part, produces 
some other effects also besides the one that 

1 . n . 1 , Each complex 

is chiefly conspicuous ; and no two causes Antecedent has 

1 £0 J. !_• T_ ■ n i? ^T_ several Effects. 

ever produce eflects which are ail oi them 
precisely alike in all respects. Hence the physician is 
to look for the other effects, or " symptoms," as he 
will call them, until he finds one or more that is pecu- 
liar to one of the causes of headache. This one 
becomes, what Bacon proposed to call an experimnen- 
turn crucis^ or a test fact. And in the pur- Experimentum 
suit of such a test, he will often find it neces- "''''^^• 
sary to experiment with tests voluntarily applied, as 
well as to observe the facts that already exist without 
his procurement. 

1026. In our attempt, to reason into the future of 

12^ 



274 LOGIC. — PART n. [chap. 

human conduct, however, the moral freedom of man 
Reasoning from ^^^ thc Uncertainty as to the determinations 
S^'moSi "^mIi- of liis will, render our conclusions pecu- 
^^^- liarly liable to error. Investigation or rea- 

soning in this way, however, is much more reliable 
when applied to masses than when applied to a single 
individual (800, 801). 



m.] ]VIETHODS OF PKOOF ANB EEFUTATIOJST. SECT. I. 275 



CHAPTEE in. 

OF METHODS OF PEOOF AND REFUTATION, 



SECTION I, 

Of Proof. 



1027. Methods of Proof presuppose both terms of 
the Proposition, whereas, as we have seen, Methods of 
Investigation presuppose merely the Subject. 'By 
Proof, then, we mean the establishment of the Proof. 
Copula, affirming or denying the relation between the 
given Subject and Predicate. From what has been 
said (431), it is evident that no proof is required of 
Intuitive Judgments. Hence in all our inquiries into 
Methods of Proof, we are understood to have reference 
to the Proof of Deductive Judgments only. 

1028. In the preceding Part of this Treatise, we 
have examined the ways in which Cognitions and Judg- 
ments can be so combined as to serve as 

Means of Proof. We have here now to con- usini tie For- 
sider the ways m which these Means or For- ^"^ ^' 
mula may be used, with an especial reference to the 
Matter on which they are to be used. 

1029. I have already remarked that Methods of 
Investig-ation are, to some extent, Methods 

J* -Ti J? 1 T T J.' X' J. Methods of In- 

01 1 root also. In Investigation we expect vestigation to 
to find as the result, that with which we start M^hods^"" ^of 
as a Proposition in Methods of Proof But 
besides being thus in respect to Methods the converse 



276 LOGIC. — ^PAKT n. [chap. 

of eacli other, their Differentia as Alternate Species of 
Methods is as stated above ; the one gives (Whately 
would say proves)^ the Major Terms, and the other 
proves the Copula. f 

1030. Methods of Proof may be either direct or 
Direct and In- indirect. Dlrcct Methods prove the Propo- 

of proof.^ "^ ^ sition to be established ; the Indirect prove 
its contradictory to be untrue, from which we have the 
desired Proposition by Immediate Inference. 

1031. Direct Proof is effected by whatever Means 
Direct Proof, or in whatcvcr Method, wherever we show 
that the Subject of the Proposition has or has not the 
essential matter of the Predicate. Since whatever has 



* Rhetoric, Part. I. Chap. I. § 1. 

t We have in popular use the words Induction and Deduction, which 
are understood to denote Methods of Proof the reverse of each other. Both, 
however, may he regarded as Methods of either Investigation or of Proof, 
since even Deduction may give a new Major Term for a subject (see Part 
II. Chap. III. Sec. III.) ; and the word Induction is also used to denote a 
Method of proving the truth of the generahzation which it effects. But 
the contrast between the two Methods in the common estimation just 
referred to, is between Induction and Deduction as Methods of Investigation. 
No contrast or comparison between the former as a Method of Investiga- 
tion, and the latter as a Method of Proof, would ever be made with any 
view to a disparagement of either Method. The contrast for the disparage- 
ment of " the Deductive Method," as it is called, was undoubtedly occa- 
sioned by the misuse of it as a Method of Investigation, which seems to 
have had its origin to some extent at least in the " Organxm^^ of Aristotle; 
and was encouraged by the schoolmen and philosophers generally until the 
time of Bacon, the famous author of the " Novum Organxm.^^ 

But there is no occasion for such a contrast. Induction as a Method 
of Proof is itself deduction from the very necessities of the case, as we shall 
see in our inquiry into the grounds of its validity as a Method of Proof. 
But regarded as Methods of Proof, Induction and Deduction differ in one 
of their more obvious properties which has not yet been mentioned. 

In Deduction the General Principle or Major Premise is most conspi- 
cuous and will be made most prominent. In Induction the particular facts 
or cases — that is, the Minor Premise is made the most conspicuous. So 
that Deduction and Induction are both of them for the most part made by 
means of Enthymemes ; the former suppressing the Minor and the latter 
the Major Premise. In Deduction the inclusion of the Minor Term or 
Subject of the Syllogism in the Subject of the Major is considered too ob- 
vious to need express statement. In Induction the general principle of all 
Induction — the uniformity of Nature is assumed as too obvious and un- 
disputed to require explicit recognition. 



ni.] METHODS OF PROOF AND REFUTATION SECT. I. 277 

the Essentia of any class, is of necessity included in that 
class, and vice versa. To render Direct Proof possible, 
therefore, two conditions are necessary : — ^g two requi- 
(1) that the Proposition to be proved must *^^^^- 
have a Positive Term for its Predicate ; and (2) that 
there may be a conception occupying a middle posi- 
tion in Logical Quantity between its Subject and its 
Predicate. 

1032. Without this last condition the Proposition 
must be either intuitive (431), or incapable of proof. 

1033. Thus for the first case — Every Effect has a 
Cause. This is something more than a simple Propo- 
sition in A, as stated ; for it results from the 

nature of the Matter, that whatever has a with noSSil 
cause is an effect. Hence the Subject " every ^^^' 
Effect," and the Predicate " has a Cause," are coex- 
tensive spheres, and both distributed. Hence there 
can be no Middle Term in Logical Quantity between 
them. The one is not included in any species which 
is comprehended by the other.^ 

1034. For the second case, take any Proposition 
which affirms what is not true, as " apples 

are gingerbread." It is seen at once that capabi?^"^ '"/ 
although these articles may be made coor- 
dinate species in a comprehending genus, as "food^^ 
for instance, yet in no way can one of them be made 
to be a comprehending sphere to the other, and conse- 

* We may, however, need to have the terms of an Intuitive Judgment 
defined or explained before the mind can assent to them. This processs, 
however, is not to be mistaken for, or confounded with, proof of the Proposi- 
tion expressing the judgment. Thus in the case above given, one would 
hesitate at the judgment until he might obtain an adequate conception of 
what we mean by *' cause," and what by " effect." In that case he would 
be in want rather of instructimi than of proof. 

And such in fact will be the case universally when one of the terms is 
but a synonyme of the other, or both are but alternate conceptions of the 
same subject (460). In this case the Syllogism which we may construct is 
rather for instruction than proof, designed to explain our terms rather than 
to prove that the Predicate may be aflarmed of the Subject of the Con- 
clusion. 



278 LOGIC. — PAET n. [chap. 

quently there can be no conception coming between 
them in Logical Quantity. 

1035. Without the first condition, namely, that the 
. propositipns Propositiou to bc proved must have a Posi- 

predicftef^*'''® tive Term for its Predicate, there can be no 
direct proof, since Positive Terms only denote their 
spheres by their matter (134). Hence if the Predicate 
be not Positive it has no matter, or rather it gives 
none, by which we can determine whether the given 
Subject be included in it or not. 

1036. The Indirect Proof depends upon the Prin- 
indirect Proof ciplc of Excludcd Middle (400), and is ac- 
complished by proving the falsity of the contradictory 
of that which we wish to prove. But as the contra- 
dictory of an Affirmative is always Negative, the Indi- 
rect Method is seldom used to prove Affirmatives, 
except in three classes of Propositions, which do not 
admit of the direct Method ; namely, (1) Intuitive 
Judgments ; and (2) those in which the words " infi- 
nite " and " eternal," &c., are used as Predicates ; or 
(3) Affirmative Propositions with Negative Predicates. 

1037. It has commonly been held, that Axioms 
Axioms inca- cxprcssivc of lutuitivc Judgmcuts ajpriori^ 

\lzi\xooi. ^' are incapable of proof. This must be under- 
stood of Direct Proof only — for of Indirect Proof they 
all admit. It consists in this case in showing that the 
May be proved coutradictory violates either the Principle 
indirectly. ^^ Identity (422), and Contradiction (423), 
or of Sufficient Cause (425). If it violates the first it 
destroys the Subject (784 and note) ; if the second, it 
involves an absolute scepticism or unbelief, by im- 
peaching the veracity of our means of knowledge. It 
thus removes the very foundation upon which we can 
pretend to know any thing ; and so the very ground 
upon which we would base the assertion by which we 
seek or expect to accomplish our object. Thus if one 
denies the proposition, " the foliage is green," he 
asserts a proposition contradictory to the sense of 
sight, concerning matter in regard to which we have 



m.] METHODS OF PROOF AND REFUTATION. — SECT. I. 279 

absolutely no means of knowledge but the sense of 
sight. Hence if that sense cannot be relied upon, his 
assertion cannot be relied upon, and we know nothing 
of colors. And so of all other propositions asserting 
the primary sense-perceptions. 

1038. The words " eternal " and " infinite^^'^ have 
been sometimes regarded as Negatives. At 

others they are claimed as Positive. But for infinfteLe/^ 
all the purposes of deduction, they can be 
used only as though they were negatives. They pre- 
dicate of the Subject no essentia, except the absence of 
bounds or limits in Continuous Quantity.. — Hence 
" eternal," " infinite," Negative and Privative Terms 
generally, are all in the same category. Denoting no 
sphere by means of its essence, they can be proved of 
a Subject only by the Principle of the Excluded Mid- 
dle. We predicate of the Subject the Positive Term, 
which is coordinate to the Privative or Negative, and 
thus show that it has not the Essentia of that Positive. 
Thus if we say, " Space is infinite," we sup- 
pose that space is " finite," or " has a limit ; " referenStothe 
that is, a limit in Continuous Quantity. If ^^^ *'^"^^' 
so, beyond or outside of this limit space is not or it is 
not space. But even if it is occupied by material sub- 
stance, it is still space ; and we have space occupied 
and space unoccupied. Hence the judgment that that 
which is outside of any limit is not space, is a contra- 
diction in terms. K it be not space, there is no such 
' outside of the limits." Hence as the Proposition, 
" space is finite," is absurd, a contradiction in terms — 
its contradictory, " space is infinite," must be true. 
In the same way all Affirmative Propositions with 
Negative or Privative Predicates must be proved (429). 

1039. If, however, the Predicate be a Positive Term, 
and the Copula Negative, we still have the positive pre- 
Essentia of the Predicate given, and must f^lf ^"jj^|: 
prove that the Subject has not that Essentia, °'^"^' 

if so be it has not, by either Observation, Testimony, 
Analysis, or the Abscissio infiniti / since none of the 



280 LOGIC. — TAUT n. [chap. 

other Methods of Investigation give negative results 
directly, or in any other way than by Immediate Infer- 
ence on the ground of the Excluded Middle. We can 
neither count, nor measure, nor average what is not. 
Induction, Analogy, Example, and Elimination are all 
based upon the properties which the objects of inquiry 
do possess, and not upon those which they do not. 

1040. But Testimony comes at last to Observation 
and Authority. The Abscissio is based upon Observa* 

Proved only tiou aud Aualysis. And Analysis of Objects 
Aumority?^'''OT is based upon Observation ; and Analysis 
Analysis. ^f Conccptions upon the Intuitions of the 

Eeason. Hence in the last analysis of our means of 
proving Negative Propositions with Positive Terms for 
Predicates, we have Observation, Authority, and An- 
alysis — Methods which give both the Predicate and 
the Copula in the one act and at the same time. 

It is a question which it will often be important to 
have answered, when are we to regard any Proposition 
as proved ? 

1041. Most Premises will be Conclusions of pre- 
premises for vious Syllogisms ; that is, they will be them- 

DeduXveJud^ sclvcs but Dcductivc Judgments — and so 
°^^"^^- lead us to consider the Premises from which 

they are deduced. 

1042. But there can be no infinite retrogression. 
There must Wc must comc at last to something; that 

be first Princi- . -, j/t jT\ • ti 

pies. cannot be proved (directly), simply because 

there is no Middle Term that can come between its 
Subject and Predicate by which it can be proved. 
Such are Axioms or Intuitive Judgments. When we 

have got back to these the mind is satisfied. 
satisfied""'"with The question, Why ? which always implies 

a belief in an anterior judgment, will and 
can be no longer asked. The judgment is intuitive, 
and affirmed by all minds as soon as the cognitions 
of which it is composed are apprehended by the 
mind. 

1043. Yet in practice we seldom need to go through 



m.] METHODS OF PEOOF AND REFUTATION. — SECT. II. 281 

this whole process. We may always assume something 
as known and admitted — something as hav- ^ practice we 
ing been already proved to the satisfaction DeduSjud? 
of those whom we address ; and which, con- °^®"^^- 
sequently, like the succeeding theorems in Mathematics,- 
are as certain to those who have been over them tho- 
roughly, as the ultimate axioms and facts themselves. 

lOM. But as we have seen already (186), it is un- 
important whether we come to an ultimate pacts and 
fact, or to an Intuitive Judgment or Axiom ; ab'^'^nto^each 
for the fact can always be transferred into a *^*^^^- 
judgment by predicating of its sphere, any one of its 
properties which we wish to make the Major Term to 
a Syllogism. 

SECTION II. 

Of Deinonstration, 

1045. The words ''Demonstration'^^ and "demon- 
strate^'''^ are often used in popular language, Popular sense 
with reference to the absolute certainty of Son. ^""^"^ '^" 
the conclusion, rather than to denote the method of 
argument by which it has been attained. 

1046. Demonstration, however, in the proper sense 
of the word, is that Method of Proof in which gtrfct sense of 
we establish the truth of a Proposition by ^^® ^*'''*- 
means of the matter necessarily contained in the con- 
ception of its subject. Hence the Predicate mu"st always 
be either (1) a Material Property, in which case the 
Proposition expresses an Intuitive Judgment which is 
analytic a priori ; or (2) an Implied Property — and in 
that case the Proposition represents a Deductive Judg- 
ment which is synthetic a priori. 

1047. In each case the judgment is a priori^ and 
implies an analysis of the conception. In 

the lirst case it affirms what is g-iven in the Analysis, "and 

T . ji • J.1 J^ '1. rr> 1 J constructed of 

analysis ; and m the second it ainrms what intuitive judg- 

is seen, on analysis, to be implied in the mat- ""^^ ^' 

ter of the conception. And the judgments at each 



282 LOGIC. — PAET n. [chap. 

step, from the analysis to the conclusion must be intui- 
tive ; and of course capable of proof, on the Principle 
of Identity and Contradiction. 

1048. In practice, however, we for the most part 
Use of pre- adopt a prcviously made analysis of the con- 

tfons"5 ^''^^^^^' ception ; and instead of taking each of the 
steps, one by one, we adopt the results of previous 
demonstrations. Thus in the successive Theorems in 
Geometry, we adopt the results of the analysis — that 
is, the Definition — given in the first two or three pages ; 
and in each successive theorem, we adopt as our 
starting-point some proposition proved in a preceding 
theorem. 

But beside the Analysis of Conceptions we have 
also the meaning of words, or force of terms^ as it is 
sometimes called, furnishing us the matter for demon- 
strations. 

1049. The force of terms or names is often very 
Arguments OTcat lu determining^ our conceptions of 

from the force Vi . t . , .t , . , j -i (* 

of Terms. thiugs, and m contributing to our stock of 
knowledge. Most names instead of being an arbitrary 
sign for the representation of things, have an etymolo- 
gical force or meaning from which we can draw some 
inference as to the idea which they are designed to 
convey — the conception of the thing itself, which was 
in the mind of the persons- who first gave the name to 
the thing. This is sometimes called the Argument or 
Inference, ex vi tei^mini. It is however strictly demon- 
strative. 

1050. Demonstrations, ex vi termini^ may be based 
Based upon the either (1) upou the necessary matter of the 
woS!^ ^^^ "^ ^ term, or (2) upon its etymology, or (3) the 
common acceptation of its meaning. 

1051. We have already seen (212), that whatever is 
On the neces; contaiucd iieccssarily in a term may be pre- 

thZteTrS/^"^ ° dicated of that term. Thus it is ex vi termini 
that a triangle has three angles — that a quadruped has 
four feet, &c. 

1052. And universally the Essentia of any class, 



ni.] METHODS OF PROOF AND EEFTTTATION. — SECT. II. 283 

considered as a genus, may be predicated of any indi- 
vidual of that genus. In necessary matter 
this ground of predication, moreover, extends tween "^^"nlces- 
to all the properties which are common to tfiJIen^" matter 
the class ; as from the nature of the matter '° ^^'^ respect. 
there can here be no exceptions to a general rule — all 
triangles must have three angles and three sides — and 
the sum of their angles must be equal to two right 
angles, &c. 

1053. But in Contingent Matter this ground of 
Demonstration must be regarded as most strictly lim- 
ited to the Essentia of the class. Otherwise it might be 
applied to an exception from the general rule and result 
in error. 

1054. "When this argument is based upon the ety- 
mology of the word, we must take heed to the changes 
which words undergo in their signification, 

by lapse of time or the peculiar circum- basef^^'^Vty- 
stances of their use. Thus allegiance is ad °*^ ^^^ ""^^ ^' 
legem^ to the law. But if one should argue, ex vi ter- 
mini^ that therefore it does not bind him to his king or 
chief magistrate, he would err about as widely as if he 
should argue that because Mr. Mason is Speaker of the 
House of Representatives, he is the man who does all 
the speaking in the House. 

1055. The conclusive force of this argument is of 
course still less, where it is based upon the , , 

, , . /? , 1 •"■ . r* Those based 

mere common acceptation oi the meamng* oi on the common 

o 1 • Pi • ^ meaning of 

terms, buch meanings are oiten given or words stiii more 
taken very much at hap-hazard, or varied 
when they have once been given by very insignificant 
and accidental circumstances. 

1056. In order to the absolute certainty which the 
Demonstration is capable of producing, it is , • f 
necessary that there be no mistake in regard an absolute cer- 
to the Material or Essential Properties of the 
Conception from which we demonstrate. And in Ma- 
thematics there is for the most part no dift'erence of 
opinion in regard to them, and of course no possibility 



284 LOGIC. PAKT II. [chap. 

of mistake ; the essential properties of a triangle, or a 
circle are the same in the estimation of all men. Every 
class-conception of necessity has such properties. 
Reason why it But in thc class-conccptlons which we form 
iT"conting^n^ ^^ objccts in the reality of being, there is 
Matter. always also some contingent matter includ- 

ed ; and hence there will be diversity in the estimates 
which men will form of the properties included in 
the conception — some regarding those as essential, 
which others will regard as merely accidental and 
contingent. In this fact is great liability to error, and 
the great som^ce in fact from which errors in Demon- 
stration proceed. 

1057. We must also remember that a property 
which is only accidental to the conception of an object 

for one purpose, may become essential to its 

Accidental Pro- i* i? i:i 7^' Zj 77 

perties become conccptiou lor auothcr. Jitg/it-angCeanesSj 
necessary. ^^^^ cxamplc, is accidcutal to the conception 
of triangle, but essential to the conception of the class 
or species which we call " right-angled trianglesP So 
" unsupportedness " is purely accidental to the concep- 
tion of ponderable bodies. But it is an essential pro- 
perty of the class-conception, formed for the purpose 
of investigating and proving the fact, and the law of 
gravitation. 

1058. And as a general rule, we may say that any 
General Rule, property bj" mcaus or on account of which 
we may include its substance in any predicate, is an 
essential property in the conception which we form 
of that subject with reference to the use of that pre- 
dicate. 

1059. When we enlarge the matter of any class- 
increasing the conception, and thereby narrow its sphere 

Necessary Mat- i . i . . . i "^ . . -*■ . i 

ter, enlarges the by taking luto our class-couceptiou another 
monstmtlon. ^ as a Mateifial property, we are enabled to 
proceed still farther and demonstrate still other implied 
properties, which have beeu brought in by means of 
the newly admitted Material property. Thus, suppose 
to the Material properties of triangle, which are two, 



ni.] METHODS OF PROOF AND REFUTATION. SECT. H. 285 

three-sidedness and three-angledness^ we add the one 
more, right-angledness. We now have a narrower sphere, 
but we are able to demonstrate many properties of 
right-angled triangles — the species — which we could 
not demonstrate, and which were not true of triangles — 
the genus merely. 

1060. But besides Mathematics, a large part of As- 
tronomy, Mechanics, and what are called Demonstration 
the Mixed Sciences generally, are largely ^"^ ^" sciences. 
indebted to Demonstration. The same is true in Logic, 
in Ethics. These are, and of necessity must be to a 
very great extent, if not wholly a ^priori and demon- 
strative sciences. 

1061. Logic has especially been called " the Mathe- 
matics of Thought." And in Logic, as in in Logic. 
Mathematics, we must prove the legitimacy and force 
of both our Formulae and our Methods a priori^ before 
we are entitled to place any confidence in the Conclu- 
sions or results to which they may lead us. 

1062. We have already remarked that Arithmetic, 
Algebra, and the Calculus, are but Methods of Inves- 
tigation in Discrete Quantity (883). But we 

are obliged to justify the Methods by De- be justitfe?1>V 
monstrations. Take the Kule of Addition, ^°^°"^ '*^"^"- 
of Subtraction, of Multiplication, of Division, of Invo- 
lution or Evolution, or the Binomial Theorem, or any 
other, and we see at once that they are but Methods 
of finding results. But the Methods are all justified a 
priori^ by inferences from the Necessary Matter of the 
Conception ; that is, from the Material Properties of 
the Methods themselves. We say, for example, that 
the square of any Binomial, as <3^ -f J, is the square of 
the first term plus twice the product of the two, plus 
the square of the second, or d^ + ^ab + V^. And this is 
shown to be true from the nature of the Process or 
Method itself, as will be seen by a reference to any 
treatise on Algebra, where the Binomial Theorem is 
discussed. 

1063. So in Ethics. We lay it down as a rule that 



286 LOGIC. — TART n. [chap. 

the communications between man and man should be 
Demonstration based upou vcracity and benevolence. We 
in Ethics. prove it from the class-conception of society, 
having proved or assumed that man, as a species, can 
live only in society. Thus, suppose the contrary, that 
deception and hate were the conditions or laws of 
human association. Deception and hate would destroy 
society, not only by rendering association among men 
impossible — but hate would take the life of man, begin- 
ning with the weakest and most defenceless, until only 
one, and he the strongest, were left alive. But one 
does not make " society. '^'^ Hence, on the principle of 
contradiction (422), we affirm veracity and benevolence 
to be necessary rules of morality. 

1064. The same holds true of all class-concejotions 
in every department of knowledge. There are certain 

Demonstration propcrtics uot contaiucd but implied in the 
mentLfknow- class-conccption, which may be predicated 
ledge. Qf every individual comprehended under that 

conception. I have instanced the laws of Motion as 
predicable on the class-conception of Matter (791). 

1065. In Theology, also, we may predicate " sin " 
of the class-conception, man, as a being having the 

Illustration powcr of clioicc, finite in capacity, sur- 
from Theology, rouudcd by objccts of desire, some of which 
are prohibited. 

1066. Now in every department of knowledge, just 

Sciences be- in proDortiou as our class-conceptions be- 
come a matter i».»iir»»i it ,»ii 

of insight as comc Qistiuct, deilnite, and adequate, mclud- 
mofe perifect. ^ ing all that belongs to the class-conception 
and nothing that does not, does our knowledge of the 
objects in that department become a matter of insight, 
or of a priori intuition and affirmation. And upon this 
part of what we know of the objects in any science, 
does the science itself depend for its existence as a 
science. 

1067. It is worthy of note that Demonstration being 
conciudSiTfrom occupicd with necessary matter exclusively, 

"we may have a universal conclusion when, 



Particular Pre 
mises. 



in.] METHODS OF PROOF AND REFUTATION. SECT. H. 287 

as is usually the case, the Minor Premise is Particular, 
or rather Individual, including in fact only one instance. 
Thus in regard to the side of the triangle,"^ and the 
position of a straight line,f we have no hesitation in 
including in our conclusion all sides of all possible 
triangles and all possible straight lines, although in 
our demonstration our attention may have been con- 
fined to a single case alone. This results from the 
nature of the matter, and is more obvious in general 
practice than in the statement just made, for then a 
diagram is usually drawn, and the line, &c., is desig- 
nated as line AB, or by some other such sign. 

1068. It is obvious from this slight examination 
that Demonstration is not a Formula, but a Demonstration 
Method in which any Formula may be used ^hfch^any fo" 
as bests suits the taste or the matter at our f^f ^^^ ^^ 
disposal. 

1069. It should be distinctly observed, however, 
that nothing accidental enters into the De- no contingent 
monstration — that is, nothins: except what info the ^scop"^^ 

.,1 , . -1 •! • T 1 01 Judgments 

was either contained or necessarily implied in the process 
in the class-conception of the subjects of the tion. ^"^°"*^*" 
several propositions. Thus when we speak of a tri- 
angle, all the matter that is contained in the conception 
is " a figure made by three straight lines so meeting 
as to make three angles." The Difierentia right-an- 
gled, isosceles, equilateral, scalene, &c., does not enter 
into the Demonstration, concerning triangles merely. 
But as triangle is the genus which includes all of these 
species, when we have proved the proposition of the 
genus, it must hold true of every included species. 

1070. The Demonstration, moreover, holds true only 
of the reality of truth, represented by the Conception, 
and not by any means or necessarily of any diagram 

* " Any one side of a triangle is less than the sum of the two other 



t " A straight line let fall from any point without a straight line per- 
pendicular to that line is the shortest line that can be let fall from the poiat 
to the straight line," 



288 LOGIC. — PAET n. [chap. 

which we may draw, or of any piece of matter which 
may be brought into the form of a triangle. For not 
the diagram nor the piece of matter was the subject of 
our Demonstration ; they serve only to illustrate and 
represent it at most, and the conclusion holds good of 
them only in proportion as they conform to the con- 
ception. 

1071. An Hypothesis, as we have seen (827), is a 
Hypotheses suDDosition or fi-ucss put iuto the place of a 

fraudulently ^ ^J^ • i ^ i • . i j. F i? 

used. tact or a judgment, m the structure oi an 

argument or system of any kind. 

Of the case in which hypotheses are unintention- 
ally mistaken for facts or ascertained truths, or of 
those cases in which they are intentionally but fraudu- 
lently and surreptitiously introduced instead of fact 
and truth we have nothing here to say : the first consti- 
tutes a fallacy in matter, and the latter is a mere trick 
of sophistry. 

1072. But there is a legitimate use of hypotheses in 
Demonstrations. Thus in Mathematics we have a 
theorem enunciated — we suppose cases, for the sake of 
testing it. We may suppose the contradictory of the 
theorem and disprove it, thus proving the theorem. 

Or we may suppose various cases to test the 
tiesreK'Ne- comprchensivcness and adaptability of the 

cessary Matter. , ^ , ^ * i. :\ t'Iij^x i 

principle enunciated. In the nrst-named 
case either the hypothesis or the theorem is impossible 
and absurd, and the method adopted enables us to 
determine what is absurd and by consequence which 
is true. In the last case the only limit to the right to 
make suppositions is that they be possible. For as in 
necessary matter there can be no exceptions, so any 
rule or principle must meet all conceivable cases com- 
ing under that rule or principle. If, therefore, we can 
suppose one that is possible, it is just as good for the 
sake of any argument claiming to be based on a priori 
grounds, as if instead of being merely supposed, it were 
actually real. For in necessary matter all conceiv- 
able things are possible, and so must be included 



in.J METHODS OF PROOF AND REFUTATION. SECT. H. 289 

within the comprehensiveness of the class-concep- 
tion."^ 

1073. But in contingent matter it is far otherwise. 
Here we are hardly competent to judge of Notsoincon- 
the possibility of what may become or may *"'^^"^ ^^"^'*- 
have become real. And in moral matter the danger 
of resorting to hypotheses is still greater. 

1074. In contingent matter we may use hypotheses 
or supposed cases for the sake of illustration. Legitimate use 
But even then we must be careful that they f^ ^SiS 
are not only supposable but also possible. ^^"®'^- 
We never do and never can understand sufficiently the 
designs of the Creator and the limits to the possibility 
of the realities of being, to be very confident in our 
opinions as to the possible and the impossible in con- 
tingent matter. There are always influences and prin- 
ciples at work of which we know but very little, and 
others of whose very existence we know nothing, ex- 
cept the constant appearance of unaccountable events 
and facts — events and facts which in our ignorance of 
these principles we ascribe to chance — to render a 
resort to hypotheses as elements in the construction of 
arguments and sj^stems in all cases of contingent mat- 
ter unsafe. 

1075. From the account which we have now given 
of Demonstration, it will be seen that while 

• nr j_i j^' T • Demonstration 

m some cases, as m JVlatnematics, Logic, in aii Methods 
Ethics, &c., it will constitute the whole of 
the Proof, it will also enter more or less extensively 
into all the other Methods as subordinate parts. For 
in all there must be some reliance upon or reference to 
the force of the terms, some analysis and development 
of the matter necessarily contained or implied in the 
conception of the subject of the Argument. It is this 
part of an argument which gives it much of what it 
has of clearness and cogency. If it does not give the 

* In fact it lias been held by one class of philosophers that Mathema- 
tics is based wholly on hypotheses. 

13 



290 LOGIC. — PAitT n. [chap. 

argument force, it makes the force which it has, felt, 
and often carries conviction where it would not other- 
wise be produced. I know of no illustration of this 
remark so good as is to be found every where in Web- 
ster's Argumentative Speeches. And no mind, so far 
as I have known, has ever surpassed his in the capacity 
to see what was necessarily contained or implied in 
the conception of any subject, and to develope it with 
overwhelming force of conviction. 

1076. And in all sciences it will be found that 
before the facts can be constructed into a science at all, 
some fundamental Principles or Axioms'^ 
all fdlnces as must bc cvolvcd by analysis of the concep- 
fundamentai^^ tlou of subjcct-mattcr, and proved by De- 
monstration. Methods of Investigation may 
be necessary to precede this step in order to give us 
adequate conceptions of the subject-matter from which 
to evolve and demonstrate the fundamental principles. 
But these principles themselves must be demonstrated 
a priori before the science can receive any permanent 
or satisfactory form. 

SECTION m. 

Of Deduction. 

10Y7. By Deduction we mean the Method or Pro- 
Deduction, cess of proving a Proposition with a less 
comprehensive subject, as a Conclusion from one with 
a more comprehensive subject, by the subsumption of 
the less under the more comprehensive— the Predicates 
of both being common. Thus in Barbara : 

M is P, 

SisM, 

.-. S is P. 

* The difference between an Axiom and a Maxim is, that the latter is 
a general truth obtained by classification and induction to a maximum 
genus ; whereas an Axiom is a necessary truth, and may be either intuitive 
or obtained by demonstration froni the necessary matter of the class-con- 
ception of ^he subject. 



in.] METHODS OF PROOF AKD REFUTATION. SECT. IH. 291 

Here S is subsumed as a class under M in the 
Minor Premise,- whence it follows that M is the more 
comprehensive Sphere of the two, and that P is predi- 
cable of S if it may be predicated of M. 

1078. Deduction forms a large part in the develop- 
ment and completion of any science. A few ^he sphere of 
leading principles are ascertained from ob- i^eduction. 
servation and experience, and from them deduction is 
made to particular facts with much more ease and 
certainty even, in most cases than an observation of the 
fact itself could be made. And in many cases, as in 
Physiology, the fact is beyond the reach of any ob- 
servation ; or in others, as in Astronomy for instance, 
it will not come round in centuries perhaps. Thus the 
details of any science will be made out to a consider- 
able extent by deduction from its general principles. 

1079. In the practical application of sciences the 
Method is always deductive. Even those 

books which are written with the most espe- aiwa% ^dedui^- 

• TP . 1* J ' 1 j^» iive in the ap- 

ciai reference to application to practice, never plication of set 
do and never can mention and enumerate all 
tlie individual cases. The most they can do is to 
specify classes of cases, and the more nearly in their 
enumeration of classes — that is, in their division and 
classification — they approach to the Injlma Species^ 
the more practical do they become in the ordinary 
sense of the w^ord. 

1080. In that case the Infima Species is the Middle 
Term, the particular indi^ddual case to which the ap- 
plication is to be made is the Minor Term, and the 
other term, whether Subject or Predicate, which enters 
into 'the " Precept," as it is called, with the Infima 
Species as the Middle Term, is the Major Premise. 

1081. Thus the physician examining a patient 
decides the case to be intermittent fever, mustration in 
His science has taught him that quinine is Pharmacy. 
required in intermittent fevers. Accordingly he pre- 
scribes quinine. His reasoning, stated at length, is as 
follows : 



292 LOGIC. — PAET n. [chap. 

Intermittent fevers require quinine ; 
This case is an intermittent fever : 
.•. This case requires quinine. 

1082. It will be seen at once that this is precisely 
the form in which the principles of science are applied 
to useful purposes. 

1083. In the same way established principles and 
In Astronomy, laws are applied to new cases. For exam- 
ple, in Astronomy the laws of motion, the relation of 
distance to time in the periodic revolutions of planets, 
comets, &c., are so well known that the moment a new 
one is discerned, the astronomer proceeds by way of 
demonstration to determine from those elements of its 
sphere nearly all that can be known about it, without 
waiting for the much slower and more tedious process 
of observing these revolutions, as they occur in the 
course of centuries of our years. 

1084. It will have been observed that one leading 
,Aii Sciences objcct iu Mcthods of Invcstigation is to de- 
deduSfve °^°a! tcrmiuc definitely and adequately the class- 

they become , . i • i ^ i ji , 

more perfect, conccptious wuicu arc Dasca upon the nature 
of things in the reality of being. It has been remarked^ 
that just in proportion as any science progi^esses from 
its inception and the first rude accumulation of ele- 
mentary facts, does it become more and more deductive 
and even demonstrative in its Methods. Our class- 
conceptions of its subject-matter by this means become, 
more distinct, definite, and adequate — more conformed 
to the constitutive Idea of the classes, more compre- 
hensive of individuals and of phenomena — and our 
confidence in the results and teachings of that science 
become proportionally great. 

* Mill's Logic, Book II. Chap. IV. § 6.— See also Devey, Book V. 
Chap. I. §. 5. 



in.] METHODS OF PROOF AND KEFUTATIOK. SECT. IV. 293 

SECTION IV. 

Of the Argument from Authority, 

1085. There are many Propositions, which from 
their relating to subjects above our compre- Authority of 
hension, or from their being beyond the i^eveiation. 
reach of our observation, and differing so far from what 
we can observe and know in this state of being that 
Analogy fails to be a safe guide, can be proved only 
by an appeal to the Authority of God in the Eevelation 
which He has been pleased to make. 

1086. Then we have also another class of Propo- 
sitions in which stat pro ratione voluntas^ Authority of 
where the will of some Authority so deter- Governance, 
mining, is the ground and the only ground on which 
we are obliged to receive them as true, because they 
have been so declared by a competent authority. 

1087. Of this kind are the laws of a State, whether 
enactments of the legislature, or decisions of the courts, 
for all citizens ; the laws, canons, rubrics, &c., of a 
Church for all its members : the constitu- 

.. T Til _£» ^ , Authority of 

tions, rules, and by-laws oi any voluntary only limited ob- 
society or corporation for economical, social, ^^^ '°''' 
moral, political, philanthropic or religious purposes, 
upon the members of those societies or corporations as 
members and during their membership. 

1088. Propositions of the kind now under consider- 
ation are authority, and therefore to be received as true 
only in relation to the particular things w^hich come 
under the jurisdiction of the authority, and for those 
persons over whom that authority justly extends. 
Thus Eevelation is final to all the creatures of God 
to whom it is made ; the authority of the state to all 
citizens and subjects; that of a voluntary society to 
those only who voluntarily belong to the society. 

1089. There are some spheres in which by the very 
nature of the case this Means of Proof is made neces- 



294 LOGIC. — PART II. [chap. 

sary, and is the only one that is proper. In Statute 

Law and Theology, for instance, the dicta 

oniy^groundTn of thc proDcr Authoritv must be an end to 

some cases. i k a t 

controversy. Any arguments on general 
grounds, as to what ought to he true^ can do nothing 
more at most than to create a presumption in favor of 
any doctrine. 

1090. Besides the foregoing, the common sense or 
consent of mankind, as well as the admissions of those 

afi-ainst whom we are ars^uine;, become first 

Concessions ^. . -, c* ,^ , Pii *, -ii* 

and common priuciplcs 01 tuc uaturc 01 autuority witnm 
certain limits, and to certain persons the 
argument from the admissions of parties ex concessis^ is 
scarcely any thing more than an orgumentum ad homi- 
nem^ and for that I will refer the reader to Sec. XI. of 
this Chapter below. 

1091. But the common opinion of men is an Au- 
thority or first principle, on which a large part of our 

Extent of i^ost important deductions are based, espe- 
n\^1t\ pJni- cially in practical matters, and among those 
cipie. whose minds have never been trained to 

look into \hQ philosojyhical grounds of their actions. 

These are commonl}^ called Arguments from Com- 
common Sense ^^^^^^ Scusc, seusits GOiThmunis oiunibus^ and 
fuesTn'diiferent thcir valuc has bccu very variously esti- 

Spheres. matcd. 

1092. In matters of Religion, if man is to be 
Religion. regarded as a fallen and depraved being, it 
is to be distrusted and scanned very closely. In fact 
it can never* be used except as confirmatory of the 
Argument from authority, or as serving the rhetorical 
purpose of removing a prejudice or supposed antece- 
dent improbability. But if man is not fallen or de- 
praved, his common sense must be as infallible an 
indication of the law and will of God {voxpopidi vox 
Dei)^ as the facts and changes of the physical world 
are of His laws and will in relation to matter. 

1093. In Polity and Ethics the common sense of 
man is of more value ; for they relate to matters that 



III.] METHODS OF PROOF AND REFUTATION. SECT. IV. 295 

are more comprehensible, and which have of necessity 
been not only subjects of reflection, but also ^ poiuy and 
and moreover they have been tested by the ^^^^''^• 
experience of all and in all ages. What has been thus 
found to be best and true, is most likely to stand the 
trial to which it can be brought. The latter schools 
of philosophy have professedly regarded this common 
sense as of great value as a standard of truth. 

1094. In the Natural Sciences it has been found to 
be an unsafe guide. It always depends upon u, t^e Natural 
the appearances of things, while in many sciences, 
cases the reality lies much deeper and is often very, 
unlike the appearance. The contrast between the com- 
mon belief in regard to the motion of the Sun and the 
Earth is familiar to all, and a case in point. 

1095. But in matters which depend upon a priori 
conceptions or upon facts, the appeal to com- j^ ^^e pure 
mon opinion is out of place. By authority, sciences. 
however, in this connection, I do not mean testimony 
to the reality of facts. Such testimony we must use 
and depend upon. But testimony to a fact Distinction be 
is one thing, and opinion or inference from it'J''t"d^T^s'tr- 
the fact is^ quite another. And the differ- "'''"^• 
ence between them is one of the things which it is most 
important to notice. Testimony is the means by which 
we know what are the Principles which have been 
established by Authority. Thus in Religion, God him- 
self is the Authority ; and the Scriptures are the Testi- 
mony which make known to us what has emanated 
from that Authority. In Law, the State is the Author- 
ity ; and the statute-books and the decisions of the 
Courts are the Testimony from which we learn what 
are the laws established by that Authority. 

1096. Hence, although we may use testimony in 
the Natural Sciences, in History, &c., Au- Legitimate use 
thqrity, strictly speaking, we do not use. of 'i^estimony. 
"We use testimony as a means of ascertaining facts, 
whether they be the facts which any Authority has 
made such, as when a State enacts a law, that enact- 



296 LOGIC. — PART n. [chap. 

ment is a fact ; or whether they are the facts evolved 
in the history of man and the world, or finally the facts 
of Nature. 

1097. Yet even Testimony is often called Author- 
Testimony of- ity — an authority for believins* the facts to 

thority. ■ which it bears witness only. We speak of 
believing a fact in Roman history on the authority of 
Livy or of Tacitus, when in strictness of language we 
In what sense, mcau thc tcstimouy of those writers. This 
distinction between Authority and Testimony is indis- 
pensable to a right apprehension of Methods of Investi- 
gation and Argument in which they are used. 

1098. Testimony can prove facts only, and a law or 
an opinion only as the facts themselves prove the 

In what way opiuion. Tcstimouy may prove the acts and 
JroviTn ^opS^ words of our Lord, as recorded in the Holy 
ion or law. Scripturcs. But tlicse acts and words, as 
facts^ must prove the Revelation, and that that which 
is given as a Revelation of the Will of God is really 
His will. Testimony can prove the enactment of a 
law, or the issuing a command — but the enactment 
itself, and the giving of the command, as facts must 
prove, if it is proved at all, that the law enacted 
and the command given are laws and commands of 
Authority. 

1099. Hence in Mathematics Testimony is never 
Testimony uscd as a mcaus of Teaching or of Proof. 

of beuef.^'^^''^^ All must rest on the personal intuition of the 
learner. In the Natural Sciences we have to depend 
upon Testimony for a large part of our facts. But the 
facts speak for themselves. Testimony cannot even 
prove an opinion^ but only the fact that such and such 
an one held it as an opinion. It does not prove the 
opinion to be true ; and all that can be gained by the 
opinion of others in the fields of scientific inquiry, is at 
most a probable ground of action^ when loe must . act 
and can have nothing hetter to act upon, 

1100. Thus a physician, in a critical case, may act 
And of Action, upou a mcrc opiuiou of a distinguished 



m.] METHODS OF PROOF AND KEFUTATION. SECT. lY. 297 

physician^ provided there is no prescription for it 
which experience has satisfactorily proved, and where, 
if he does not act at all, only the worst of consequences 
can ensue. 

1101. In all appeals to Authority, and to Testimony 
also, howsoever and wheresoever expressed, Necessity for 
the true meaning of the words in which it is in^uiT^usI'^iV 
expressed is of material importance, and of Authority. 
course one of the first things to be obtained. Language 
itself is but an imperfect instrument for the expression 
of thought, and often it is used without clearness in the 
mind of him who uses it, and without any successful 
effort to make it as adequate to the expression of the 
thought as its capabilities would allow. 

1102. The process by which we evolve a man's 
thoughts from his words, is called Interpre- 

, . * TT J.* o i.1, • J? • I. Interpretation 

tation or MermeneuUGS. bomethmg oi inter- or Hermeneu- 
pretation is always necessary when we read. 
But when such words are used as we are familiar with, 
and the clear thought is clearly expressed in familiar 
phrase, the process of interpretation is performed so 
quickly and so easily, that we are wholly unconscious 
of it. It is only when it becomes diflBcult, and takes 
time, and causes delay and doubt, that we become 
conscious of the effort, and feel the need of rules and 
principles to guide us. 

A few of these leading and most important princi- 
ples we will now briefly specify. 

1103. (1) In the first place, wherever there is one 
plain and obvious meaning to a passage, that tE'i?''the5 
is to be adopted. ?^g^^«^^ "^^^"- 

Seldom, indeed, will it be expedient or allowable to 
go behind the text itself to any evidence or indications 
of what the author may have intended to say, provided 
his language is clear and appears to have been used by 
one who knew how to express whatever thought he 
may have intended to communicate. The choice of 
words and expressions was with him, and he must be 
responsible for what he has clearly and plainly said. 

13^ 



298 LOGIC. PART II. [chap. 

llOi. (2) But secondly, where language is ambi- 
Ambiguous Ian- guous, OY the meaning of a passage is doubt- 
teSfreted^^ *"" ful, wc are to interpret in accordance with 
truth and right sentiment if possible. 

• This rule is charitable enough, and may sometimes 
give one more than his due. But it is better to do so 
than otherwise. Let the error, if there be one, be put 
down to the account of charity. 

1105. (3) Thirdly, we must take heed to the usus 

quinli."'"' '" loquendi : 

{a) Of the author himself. 

(J) Of the sect or people to which he belongs. 

There is scarcely a writer or speaker who has not 
some peculiarities in style, and in the use of some of 
the words which will occur in the course of his writings 
or speeches. The exact meaning of such words, as 
used by any man, is best obtained from a study of his 
own writings ; or secondly, in case there are none, in 
those of the sect or school to which he belongs. Thus 
the word " Idea " means one thing, in Plato's use of 
it, another in Mr. Locke's, and still another in the writ- 
ings of some modern philosophers, as Kant and Cousin. 
If, therefore, we should undertake to read the writings 
of any one of these authors, with the sense which the 
other attaches to the word whenever it occurs, we not 
only should fail to find our author very clear and intelli- 
gible, but we should deduce from his statements conclu- 
sions which his words, when understood as he intended 
them^ would not justify. It would be easy to accumu- 
late a long list of words, illustrating this point, but we 
have not room. 

1106. (4) The fourth rule is, that technical terms 
Technical Terms, must bc cxplaiucd by thc science to which 
their use belongs. 

Every science has, and of necessity must have some 
terms to which those who are proficient in that science 
will attach a meaning, somewhat diflerent from that 
which it has among those who are unacquainted with 
its scientific use. The word " switch," as used by 



in.] METHODS OF PROOF AND EEFUTATION. SECT. IV. 299 

boys at their plays, and by a railroad manager, has 
two entirely distinct senses. In fact no one can read 
any treatise on a scientific subject with which he is 
unacquainted without finding new words, and old words 
used with new significations. Lexicographers, in pre- 
paring their Dictionaries, derive their definitions from 
the sources now indicated, or at least should do so. 
But in no case can a Dictionary give all the technical 
words with all their meanings. Let any one, for in- 
stance, attempt to find in any Dictionary a definition 
of the terms used by sailors at sea, by printers in the 
printing-office, to say nothing of the technicalities of 
Law, Medicine, and Theology, and he will see the 
necessity and reasonableness of the rule of interpreta- 
tion now laid down. 

1107. (5) All language used in deeds, wills, and 
other documents, conveying: property from 

. • LanfiTuaffe of 

one to another, are to be interpreted in favor giving andcon- 
of the grantor, if there is any of ambiguity. 

The obvious reason for this, is that the right of 
property requires that no one should be presumed to 
have intended to give aw^ay any more than he ex- 
pressed his intention to give. 

1108. But to this there are several modifications ; 
and the first is in conveying away any obj ec t, Modifications 
we convey wath it whatever is inseparable tothemie. 
from it, even though it be not mentioned ; and secondly, 
as a grant is seldom if ever made except for a consider- 
ation of something in return, the amount of this con- 
sideration may sometimes be taken into account to 
determine the true sense of the grant. 

1109. (6) Oaths are always to be understood (m 
sensu imponentis)^ in the sense of the au- oaths, 
thority which imposes the oath. 

Oaths are given to secure the fidelity and truthful- 
ness of those on whom they are imposed. But if those 
who receive the oaths may take advantage of any ob- 
scurity or ambiguity which may exist in the language 
of the oath itseli, or which by ingenuity and prejudice 



300 LOGIC. TART H. [CHAP. 

persons interested can cause to exist, the obligations 
of an oath and the very purposes for which they are 
imposed will be at an end. One has a right to know, 
before taking an oath, what it means and what it is 
designed to impose npon him. And although he 
would be justified in some cases in refusing the oath 
and submitting to the consequences, yet in no case 
would one be justified in taking the oath and then per- 
juring himself, under the plea that the oath is suscep- 
tible of another construction, than that designed by 
the authority imposing it, or that he chose to put an- 
other construction upon it. 

1110. (7) All laws, edicts, &c., restraining personal 
Laws, Edicts, liberty and the ris^ht of private iude-ment, 

restraining Ub- , *^-. . , , ^^ jy ^ ^ ^ *^ ® m i 

orty. are to be mterpretea as lavorably as possible 

to those who are thus restrained. 

All law and authority is of necessity and essentially 
a restraint upon the personal liberty of those who are 
subject to the law or authority. We seldom speak of 
it in this light, however, except where the restraint 
becomes greater than there is any good reason for. 
But as such restraints should be as little as the cause 
of order and morality will allow, we are to interpret 
all laws which go beyond those requirements in favor 
of the subject, and give him the benefit of any ambi- 
guity that there may be in the language in which the 
laws are expressed. 

1111. (8) Commissions and other documents con- 
commissions ferriup; authority or privile^'e, are to be 

and patents of Yt t^i*/* 

privilege. regarded as JLxclusives {expressio unius^ 
exclusio alterius). This is substantially the same as 
the fifth rule above, in a different application. No 
one is jyresumed to have any authority over another, 
or special privileges and exemptions. If he has them 
there must be proof of it, and the mention of one or 
more in the words that confer the authority or privilege, 
leaves the others in possession of no more than they 
would have had if no such document had been issued. 
The commission of one man in a company does not 



in.] METHODS OF PROOF AND REFUTATION. SECT. IV. 301 

constitute all the privates captains. Nor does the 
appointment of one man to be a justice of the peace 
make the whole neighborhood to be esquires. 

1112. (9) When the quantity of a proposition is 
doubtful we are to take it at its least value, ^j^^ Quantity 
unless the conclusions of the argument, or of a proposition. 
the truth of the statement require otherwise. 

Thus in Wayland's Political Economy occurs the 
remark, which is universal in its form, " All men are not 
TaeTchantsr But truth requires that it be considered as 
particular negative — that is, " Some men are not mer- 
chants." And again ; from the connection in which it 
occurs, it appears to have been designed as a contra- 
dictory of a supposed preceding universal affirmation, 
" All men are merchants." Again, the following oc- 
curs in a work before me, " Abstinence from eating 
flesh had reference to the divine institution of sacri- 
fice ; " the author's argument, as well as the ordinary 
principles of interpretation, require that the proposition 
should be regarded as universal. But the truth of the 
proposition would in that case be a matter of doubt at 
least, and most likely the proposition would be false if 
taken universally. But if the proposition had occurred 
where no use was made of it, requiring it to be regard- 
ed as a universal proposition, it would have passed 
without notice as a statement generally true, perhaps, 
but yet only the expression of a particular judgment, 
"Abstinence" being regarded as not a distributed 
term ; the abstract term being used for the concrete 
plural. 

1113. (10) Parables and metaphors are to be con- 
strued with special reference to the design parawes and 
for which they were used. Metaphors. 

Parables, metaphors, fables, and all of that kind of 
illustrations, are based upon analogy and not identity 
of cases. But in all analogies there are points of 
diversity, and the case upon which the parable is based 
is assumed to be identical only in the point to be illus- 
trated by it. In that point there must be identity, else 



302 LOGIC. — ^PAET n. [chap. 

the illustration fails ; beyond that point there must be 
some diversity. These points must not be brought into 
the illustration, nor may its force and appropriateness 
be objected to on their account. 

1114. In the Parable of the Rich Man and Laza- 
rus (Luke xvi.), for instance, the main design, undoubt- 
edly, was to show the impossibility of changing one's 
doom by repentance after death. And it would be 
unsafe and unwise to attempt to infer any thing further 
from it concerning the condition of man in the future 
state. We can hardly go so far with safety, (I think,) 
as to infer from it that the two classes of persons repre- 
sented by Lazarus and the Kich Man, are in a condi- 
tion to hold conversation with each other, or with those 
of the other class at all. 

1115. (11) Mere obiter dicta are never to be re- 
ohiter dicta, gardcd as of equal authority with the as- 
sertions made to the point directly before the mind. 

In nearly all discourse and reasoning there is a 
leading object, to which the attention is especially 
directed. The assertions bearing directly on that point 
are always to be regarded as the most mature and 
carefully guarded opinions of the author. But there 
are almost always expressions dropped by the way, 
called obiter dicta^ on incidental and collateral matters, 
to which the attention is not directed with so much 
energy as to the main point, and consequently these 
obiter dicta are less valuable as expressions of opinion 
or authority, than those to which the attention is mainly 
directed. 

1116. The science of Interpretation is a compre- 
. Special Rules heusivc ouc, and cannot be fully treated in 
d"ep"anLferft!'^'^^ this placc. Aud as in each special depart- 
ment of inquiry, where we have to depend upon Testi- 
mony and Authority, some special rules and cautions 
are found necessary, I have aimed above to give only 
such general rules as seemed necessary to my present 
purpose, and of the most extensive application. 



m.] METHODS OF PKOOF AND KEFUTATION. SECT. V. 303 

SECTION V. 

Of the Appeal to Facts. 

1117. The Appeal to Facts, as a Method of Argu- 
ment, is in some respects the converse of the ^pp^ai to 
foregoing Methods. We reason from Facts ^^^^• 

to Principles rather than from Principles to Facts. 

1118. These Facts may be introduced by way of 
Induction, Analogy, Example, or as Contra- pacts how m- 
ries, Exceptions,^ Circumstances, Cause or Produced. 
Effect. But in all cases they require the force of Prin- 
ciples lying deeper than the facts themselves, in order 
to render their argumentative force of any value. 

1119. I have already in the last Chapter (Section 
VII.) said concerning reasoning from Cause cause and Ef- 
to Effect — that is, concerning the appeal to ^^''^• 
Facts as Causes or Effects, all that I shall deem it 
advisable to say in the present Treatise. I will, there- 
fore, proceed at once to consider the general Principles 
involved, and the Methods of proceeding in reasoning 
from Facts in the various other conceptions of them. 

1120. An important distinction is made between a 
law and a general fact. Thus it is a general General Facts 
fact, proved by Induction, that '^ all Canidae ^°^ ^^^'• 
are carnivorous ; " — '' all bodies gravitate towards the 
Earth." But that which lies under this general fact 
and determines the manner in which the Cause shall 
act, is called the law. Hence the law of gravitation 
is that which accounts for the general facts of gravity. 
It is the law which produces, or rather guides the 
cause in producing the general fact of a carnivorous 
habit of life in animals, constituted by their Creator 

* For facts introduced by way of Exceptions, see Sec. IX. below. 
Since they always presuppose tbat to wMch they are exceptions, I have 
chosen to consider them as means of disproof ; that is, disproving the uni- 
versality of that rule in view of which alone they can be regarded as ex- 
ceptions. 



304 LOGIC. — PART n. . [chap 

for that habit of life. Hence the law always implies 
the fact and the fact the law, and the two are often 
confounded. 

1121. We place but very little confidence, how- 
ever, in any mere induction of facts, unless we can go 
Induction must ^ little farther. The Formula of Induction 
mere^ciaTsMca^ Itsclf, as wiU bc sccu (569), is an undistri- 
*^«"- buted Middle, and becomes valid at all only 

by a sort of transfer of the matter over into the domain 
oi necessary matter. 

\V2i'^, This we accoinplish by means of principles, 
logically antecedent to all induction, and lying deeper 
How accom- ^^ ^^ subjcct-mattcr than Induction itself 
piished. (3^j^ reach. By this means we can extend 

our predication from what is and has been to what 
will be. We pass from the general fact to the law.^ 

The first of these Principles which we shall con- 
sider is the Uniformity of Nature — the second is that 
of Final Causes. 

1123. We use the word " Nature " [JVatura, from 
"Nature "in nascor]^ as a collective term, including all 
used. ^^°^^ those realities of being in the external world, 
whose existence is contingent, and which are not the 
product of human agency as their Efiicient Cause. 
Thus a blow with the hand would not be a fact in 
Nature, since it proceeds from the will of man as its 

* We have given above, p. 249 w., Aristotle's definition of Induction, 
Top. B. I. Cap. XII. In the Prior Analytics, Book II. Cap. XXII. Aris- 
totle speaks of Induction as a means of proving one extreme through the 
other, i. e. to prove the Major Term oftfie Middle, by means of the Minor. 
Thus he gives for example : 

Men, horses, and mules are long lived ; 
Men, horses, and mules are void of bile. 

If then, says he, (men, horses, and mules) and (long-Hvers) may be 
converted " without excluding the Middle," — that is, if (long-hved) is not 
a more comprehensive sphere than (men, horses, and mules), we may have 
the conclusion : 

All animals void of bile are long-lived ; 

But this is the very difficulty ; the Major Premise can never be con- 
verted in that way. The Predicate is always comprehensive of more than 
the inducted particulars, and it is precisely this peculiarity of induction that 
we wish to account for and justify. 



m.] METHODS OF PEOOF AND REFUTATION. SECT. V. 305 

Efficient Cause. But the growth of a blade of corn 
would be a fact in Nature, although the growth might 
depend upon the fact that man had planted it, or still 
keeps the soil in a condition to continue its growth 
towards maturity. In this case man is not the Efficient 
but only the Occasional Cause. 

1124. By the Uniformity of Nature we mean what 
may be stated s:enerally as the fact, that the 

•^ ^^. *^ 1 . 1 1 What is meant 

same causes acting under the same laws, hy'^umformi- 
and cceteris paribus — (that is, all the modify- ^^' 
ing circumstances being the same,) will produce the 
same effects.^ 

1125. But let us try to get a little more definite 
idea of this uniformity, and the grounds upon which it 
rests. 

It is, doubtless, first suggested by the facts in the 
external world. Thus, for instance, a tree 
always produces leaves and fruit of the same uniformity how 
kind. So, too, with the offspring of animals. 
Each new individual is not the germ of a new class or 
species. Nor does it even belong to a species different 
from that from which it derived its origin. In short 
the objects of nature at once suggest the classifications, 
by means of Essentia and Diflerentia, which have al- 
ready been spoken of as so advantageous to science. 

* Mr. Mill thinks (besides expressing some doubts about the Uni- 
formity of Nature) that what we know or believe of it we have learned 
from experience. In a certain sense this is true. And using words still 
in the same sense all that we ever know is learned from experience. But 
then we may easily get to be wiser than our teacher. We learn from ex- 
perience a great deal more than there is in experience. Experience is con- 
fined to the past, and generalizations upon its facts can give us only what has 
been. But by induction from the facts of experience we infer what is to be 
in the future, and every where in the reality of being constituted like that 
in which we are placed. From mere uniformity we do not expect its con- 
tinuance, as Mr. Mill has indirectly shown. From the fact that the first 
five or six of the Presidents of the United States retired from ofiice at the 
age of sixty-six, the people of the country formed no expectation whatever 
that such would continue for ever to be the uniform fact with regard to the 
age of the retiring Presidents. Hence it is something not given in experience 
which leads us to expect a continuance of this uniformity in some cases and 
not in others. This " something," call it what you will, is what we are 
now inquiring after, and it must be apriorL 



306 LOGIC. — PART n. [chap. 

1126. But if they suggest to our minds these classi- 
fications, it must be because they proceeded from a 

^. ^ class-conception in a mind like our own, at 

ingmind essen- Icast iu rcspcct to the faculty of constructing: 

tially like ours. t ■*-.. toji it ^ 

such conceptions, li the words 1 use sug- 
gest to the mind of the reader or hearer a thought, it 
must be because they proceeded from the same thought, 
and are used as a means of expressing it in my own 
mind. 

1127. Let us then consider the operations of the 
An analogy in humau miud. Take the case of an artisan. 

the operations -pT !> iA ^ i} ' ^ i • 

of man. Hc lorms tuc plan ot a piece oi mechanism, 

a watch for instance — that plan is his class-conception, 
his object being not to produce one watch only but a 
number — a supply for the demand of his customers. 
Hence we have a species of watches agreeing exactly 
with each other, so far as the properties included in the 
class-conception are concerned, but diifering in the 
accidents of having been finished at different times, 
by different hands perhaps — made in part of diff*erent 
materials, some having gold and others silver cases, &c. ; 
and differing also in size and ornamental decorations. 
Now, suppose the same artisan to form a different plan 
or class-conception, one differing therefore in some of 
the essential parts of a watch, as in the form of the 
escapement, &c., and we shall have from that model 
another species of watch. 

1128. Now before creation, the Creative Mind must 
The class con- havc formcd such class-conceptions for each 

ceptions of the . .» , -y ^ * i ^ i-i* 

Creative Mind, spccics 01 creatcQ ODjccts; and. each indi- 
vidual in a species is like all the others in all the pro- 
perties which were included in that class-conception ; 
and differing from others only in those which, from 
their not being included in the original class-concep- 
tion, are called accidental.'^ 

* This illustration of the operation of the Divine Mind might he car- 
ried much farther. One point more only, however, will I notice in 
passing. 

It is not altogether voluntary with man what elements he will include 



in.] METHODS OF PEOOF AND REFUTATION. SECT. V. 307 

1129. We may then say that the uniformity of 
Nature consists in the agreement of all objects 
within the same species in the matter of their ity of Nature 
class-conception. And onr Induction is but 
the process by which we make our conceptions of the 
material species adequate. We get one of its elements. 
We classify upon that ; then find another property 
common to all the individuals in that species which 
have fallen under our observation — ^predicate this latter 
property of the species by means of the specific name 
which we have given it, and call the Proposition so 
made a statement of a law of Nature. It is an indica- 
tion of the Divine will and conception ; and therefore 
we expect all individuals in any class to conform to the 
essentials of that class — which essentials we are learn- 
ing one after another by Induction. If there were no 
such class-conception, there could be no classification ; 
no Uniformity of Nature ; consequently no Induction. 

in his class-conceptions. Having fixed upon some which are material to 
it, there are others that are necessarily imphed, and others that are acci- 
dental — over which, however, he has no control, any further than his own 
hand may he employed in making the objects in the class. Thus in a 
watch, if he would have a lever escapement, he must have a hair-spring, 
whether he would or not, he must have wheels and pinions to graduate the 
motion ; and he must have the hability to break, to wear, &c., as insepar- 
able from all the materials that man has at his command to use. And as all 
the watches of that species are to be made by himself, or under his control, 
he can control the purely accidental properties of size, ornament, &c. But 
beyond that he has no control over what is accidental. 

In Nature, however, there is but one Creator and Producer. All those 
properties of the objects of nature, therefore, which so far as we can see, 
are only accidental to the class-conception, are yet under the control of the 
Will of Him who designed and still produces them ; and in all of them, 
therefore, He can secure a perfect uniformity, and make them to be for all 
practical purposes, not accidental but essential. 

Hence individuals in the natural species, as apples, pears, peaches, dogs, 
horses, men, &c., &c., do not differ so much from each other, or from their 
idea or class-conception as the works of man, watches, hats, boots, coats, 
&c., &c., nor even so much as the diagrams which we draw to represent 
the mathematical figures, triangle, circle, ellipse, &c., diff'er from one 
another, even among those which are designed to represent precisely the 
same conception. Always do they come short of the conception to some 
extent, come short of realizing it as an idea ; and go beyond it in present- 
ing to the mind for its consideration, properties which were not contained 
in the conception. 



a Premise 

that 

sion 



308 Loaic. — PAKT n. [chap. 

1130. Now whatever is necessary to the proof of 
any Proposition is in some way a Premise to that 

Whatever is Proposition, Hence the Uniformity of Na- 
condSnf i! ture being necessary to the belief in the 
'Soaci^- i*csult of any Induction, that uniformity 
must enter in some way as Premise to the 
Conclusion from the Induction, when announced as a 
Law of Nature. 

1131. Using these principles as Premises, we are 
Induction com- ablc to complctc the Induction into a Syllo- 
gyibgism.^** ^ gism as follows. For Major Premise we 
have, " All similar instances in Nature are governed 
by the same law." 

For Minor Premise we may say, " The cat, the dog, 
the wolf are instances of carnivorous animals, similar 
in having canine teeth." 

.-. All animals with canine teeth, will be instances 
of the same law, viz., carnivorous animals — that is, 
" All animals with canine teeth will be carnivorous." ^ 

1132. But if the Major Premise were removed or 

* It has been pretty extensively lield that Induction is a Method of 
Argumentation totally unlike the Syllogistic, and one which can never he 
reduced to a Syllogism. Sir William Hamilton was of this opinion. Now 
there can he no doubt that Induction, as a Method of Investigation^ is a Me- 
thod radically different from Deduction or the Syllogism. But the Induc- 
tion, as an investigation of the predicates of Natural Species, is a very dif- 
ferent thing from the verification of that Method, or the use which we 
make of the Induction as a means of proof. The Binomial theorem is one 
thing, the use we make of it in practice quite another — and the reasoning 
and principles by which we verify the theorem is another still — and quite 
as distinct from the theorem itself. 

Now Methods of Investigation cannot be reduced to the Logical For- 
mula. The Formulae are the Means to be used in the Methods of Proof, 
and whatever can be proved must be proved by some Formula — one that 
has been catalogued and examined, or one that yet remains to be entered 
upon our list. But Methods of Investigation prove nothing. 

There can be no need of the accumulation of authorities or of argument 
to show, not that the Induction, but that our confidence in its results — 
and hence Induction, as a Method of Proof, depends upon the uniformity 
of Nature. This point is nowhere denied or doubted. If this be so, this 
Uniformity, stated as a Principle or Premise, must be the Major Premise 
in all Proof from Induction ; and the basis of the verification of Induction 
itself as a Method of Investigation. 



III.] METHODS OF PROOF AND REFUTATION. — SECT. Y. 309 

denied, no confidence whatever would be placed in the 
Conclusion. That is, take away the Uni- 
formity of Nature, and we should place no withouuh^Ma" 
confidence in Induction as a means of Proof, -"^^ ^^^"'''®- 
or as indicating a law upon which we could base any 
predictions or expectations for the future. 

1133. We have seen that Induction is the Method 
which most appropriately belongs to the facts in 
the reality of being, and within tne range 

of what is called Nature — including as it longsTo'physl- 
does all facts which are not considered as 
depending directly upon the will and volitions of a 
moral agent. But inasmuch as the will of man is 
subject to no such law of necessity and uniformity, as 
the course of Nature, and inasmuch as the courses of 
events in God's providential government of the world 
are to such an extent above our knowledge But not to mo- 
and comprehension, the facts or events in ^^^.i Matter. 
each of these two Spheres are hardly to be considered 
as within the province of Induction. AVe can indeed 
in this way learn much of the nature of man, and of 
the plans and principles of God's moral government, 
but not enough to enable us to speak with the same 
confidence as we may use in regard to the facts of 
Nature. That God is just, we know indeed as well as 
we know any truth of Natural Science, and that He 
will punish any particular sin we may also know with 
the same certainty. But the particular time, way, and 
means we cannot infer from any induction of the past 
with any thing that approaches a physical certainty. 

1134. So, too, from an observation of human nature, 
we see that men for the most part are s:ov- 

T . ,1 . ,. T J j_ i 1 • Moral freedom 

erned m tneir actions by a regard to tneir destroys uni- 
own interests. But we cannot therefore say, ^'''"''^^• 
in any particular case, with any thing like the certainty 
of an induction, that this man will be controlled by 
considerations of self-interest. There are not only too 
many exceptions to the rule to allow of such a cer- 
tainty, but we recognize in all men a capacity to resist 



310 LOGIC. — TAB.T n. [chap. 

all such considerations whenever they choose to do so ; 
not only for the purpose of following their passions, but 
also in many cases for the heroic purpose of sacrificing 
themselves and their own interests for the truth and 
the good of others. 

1135. The next condition, limiting the sphere of 
Induction, is that the Predicate be not an Accidental 

Induction can- propcrty, but such as are regarded as inse- 
denter^proper- pGi'^ohle propcrtics. Inductiou does not ex- 
^^^^- tend to separable accidents or j)roperties. 

If they are inseparable it is because there is some law 
or necessity connecting and binding them to a con- 
comitance with the more obvious properties which 
make up the Essentia of the class-conception. But if 
they are separable their connection with the indivi- 
duals of the genus is regarded as merely accidental, 
implyinp^ neither necessitv nor law : and the 

Properties now -^ "^ P . p i f j. ^ i i 

considered acci- conncctiou rcmaius, lor the present at least, 
fo^und t^be es^ au Isolatcd fact. Further discoveries, how- 
ever, may find relations which indicate law 
and design, and then a new genus will be formed to 
which this property will no longer be an accident but 
an inseparable property. 

1136. But until that is done and we gain some in- 
sight into the will and designs of Providence, farther 
than the mere Induction of facts can give, we hardly 
call our investigation an Induction at all. Thus M. 

Cousin has observed that OTcat events take 

Cousin's illus- ■■ • j.i • 7 77 j? j • tt i 

tration from his- placc lu the iniddie ot centuries, lie speaks 
^'^'^" of the Middle of the Fourteenth as remark- 

able for the discoveries and revival of learning ; the 
Fifteenth as remarkable for the fall of Constantinople ; 
the Sixteenth for the Reformation ; the Seventeenth 
for tlie English Rebellion, &c. ; and yet no one regards 
this as an induction establishing a law, that the middle 
of every century will be accompanied by some great 
event in history. Again, five of the Presidents of the 
United States — the first five, went out of oflice when 
they were sixty-six years old. No one regards this. 



rn.] METHODS OF PKOOF AND KEFUTATION. — SECT. V. 311 

however, as an induction that establishes a general 
fact or law, that all Presidents shall hold office until 
they are sixty-six years old. 

1137. And yet there is undoubtedly an important 
sense in which the facts of History constitute pacts of His- 
a field for inductive investigations. stftuung a fiefd 

One of the most striking and extraordi- for induction. 
nary illustrations of this that I have ever seen, is Spel- 
man's History and Fate of Sacrilege ; in which, after 
deducing the law of God upon the subject from the 
Scriptures, he runs over the whole of History, and 
especially the History of England since the Reforma- 
tion, to show how the facts of History indicates prin- 
ciples the same as those educed from the Scriptures. 

1138. This use of History assumes that God has a 
plan and a purpose in History, and 2;overns tws use of 

ti 11111 iii History assumes 

the moral world by laws as completely as a Moral covem- 
He does the natural world ; and that from wid. 
the facts evolved. His will can be learned in the one 
case as certainly as in the other. 

1139. Induction, therefore, becomes a ground of 
Proof, or belief in the result obtained by our induction ap- 
classification, only as it approaches to the D'?mon^suat?on^ 
condition in which we could demonstrate the conclu- 
sion which we reach by our inductive investigation 
from the class-conception. In Mathematics we get the 
class-conception by constructing in our own mind the 
figures which are comprehended under it. But before 
the creation of the world, the Creator must have con- 
structed the same class-conception of all objects to be 
comprehended under each species of being that He 
would create. These conceptions are what Plato called 
Ideas, and Aristotle called Notions (ra vorjTo)^ or as 
we render the word, " conceptions." 

1139. Induction helps us to these Ideas or Concep- 
tions, and puts us, so far as it is successful, induction lim- 
into the position which the Creative Mind jl|^ l^^xied^or 
occupied with regard to them before crea- ^"ghmf'^Sai^ 
tion. It puts us into the same relation in conceptions. 



312 LOGIC. — ^PART n. [chap. 

regard to objects in the natural world as we sustain 
to the Figures of Geometry, which we have constructed 
in our own imagination, or those conceptions of the 
various machines and implements of human contriv- 
ance with which the abodes of civilized man every 
where abounds. And from the matter of the Ideas or 
class-conceptions, as Material Properties, we see that 
other properties are necessarily implied. And it is a 
matter of doubt if there is or can be any Induction 
which deserves to be so called — that undertakes to 
prove any property of a species in natural objects 
which is not implied in the Matter of its class-concep- 
tion, as that conception existed in the Creative Mind.^ 

* Since these pages were put into the Printer's hand, I have met with a 
report of the doings of " the American Association for the Advancement of 
Science^'' held at Providence, E. I. In the report of the doings for August 
16th [1855], there is an account of Pkof. Agassiz' paper of " The System 
in Zoology," from which I make the extract below. 

I have long regarded Prof. Agassiz as the most philosophical of all our 
naturahsts ; perhaps more so than any other scholar in that department now 
living. And it affords me great pleasure to find that after some twenty 
years study and effort at an attempt to classify, and so proceed with his 
Induction on some other principle than that to which I had arrived on phi- 
losophical grounds, he has at last found by his experience that it is impos- 
sible to do so. And, aside from the pleasure which it affords me as a con- 
firmation of my view on the subject, I cannot but regard his announcement 
as not only a great triumph of philosophy lq general, but also of Christian 
Faith in particular. 

I give his words as I find them in the Report (N. Y. Daily Times, Aug. 
18, 1855). Even the Italics are given as I copy them. 

*' Even as late as the last classification of the animal kingdom by 
CuviER — a system which has made his name so famous — that distinguished 
naturalist depended more upon arbitrary groupings than upon critical ob- 
servations of natural affinities. To be understood well, the tnie relations of 
the system of Nature ought to be considered a^s an analysis of the thought ex- 
pressed by the Creator. Classification is in reality nothing but the expression of 
that thought. We may no longer speak of our system. We may only speak of 
our readings of that thought which constitutes the animal system ; which 
has gone on developing through countless ages. No longer do naturalists 
consider the Animal Kingdom without reference to the cause of existence. 
They are ail driven to one point. They are compelled to ascribe existence 
of animal forms, either to physical causes or to an intelligent Maker. Be- 
tween these two there is no medium point, no other alternative. The 
classes of animals are either the result of the general forces which we ob- 
serve in Nature, or they are the work of an intelligent Being. Do we see 
in these classes the evidences of physical force — or thought ! And now, 



m.] METHODS OF PEOOF AND EEFUTATION. SECT. V. 313 

Thus if carnivorousness was an element in the class-con- 
ception of the Canidge, just as equality of radii is in 
that of the circle, then canine teeth were as necessarily 
implied as a property of the Canidse, as the Formulse 
and Propositions of Trigonometry are in the conception 
of the Triangle. 

1140. We can also accomplish our object of passing 
from the facts of Nature to a law by means ^^e may also 
of the conception of Final Causes. A Final fo1aVS"^eans 
Cause, as has been defined, is that for which of Fmai causes. 
any thing is or is done. 

1141. We are conscious of acting from purpose or 
design. Our actions are conformed to our origin of the 
designs and reveal them to others. We can causesin^Na! 
also see in the motions, features, and acts of ^^^• 
other persons indications of their designs. We can 
often see in the structure of a piece of machinery or 
an implement of any kind, the design which its framer 
intended and expected it should accomplish. 

1142. Precisely so in Nature we see, and cannot 
help but see marks of design — proofs that the Mature indi- 
Creator had an end in view — that He created *^^^^^ ^^^*^"- 
from regard to Final Causes. If now we find by our 
induction that animals with canine teeth are carnivo- 
rous, and can moreover see that that kind of teeth are 
especially adapted to that kind of food, we have scarcely 
less doubt that all animals with canine teeth are carni- 
vorous, than if we had seen them all in the pursuit of 
that mode of life — or if the Omniscient Creator Him- 
self had revealed to us the fact. 

1143. When then our induction leads us to see any 
connection between the Essentia of the Ge- Final causes 
nus and the Property predicated of it, as is b?sed upon ?he 
implied in the doctrine of Final Causes, or creato?. 

as the necessary correlates of each other, we feel 

-vrhen we come to consider the Animal Kingdom practically, as a process of 
Zoological Investigation, it comes first in order to ascertain whether, in the 
combinations already ascertained, we can read that thought, or whether any 
other result can there be read." 

u 



314 LOGIC. — ^PAET n. [chap. 

confident that we have found a law, which if it be not 
based upon the necessary nature of the things, is at 
least based upon the will of the Creator, and will not 
therefore be changed while the present order of things 
remains. 

1144. But so expressive are the works of Nature 
every where of purpose and design, that long before 

Nothing made ^'^ comc to couscious rcflcction upon the 
in vain. subjcct, wc havc comc to believe that what- 

ever exists as the work of the Creator, was made for 
some purpose, or " Nothing was made in vain." The 
Formal properties — that is, those properties in any 
object which are regarded as constituting it an indi- 
vidual in the species between itself and the next sub- 
altern species or genus, which is in our minds at the 
time, put us on the inquiry to ascertain what are the 
implied properties which accompany these Differentia 
or Formal properties ; and what are they for ; what 
fact or law in regard to the individuals of their class 
do they indicate. 

1145. Now this way of regarding the Formal pro- 
perties of objects is not the result of any system of phi- 

The idea of losophy. It cxists bcforc philosophy. One 
lidsL ^heflTe <^f the first questions that the child learns to 
Philosophy. ^g]^ ^j^]^ regard to any thing new that at- 
atracts its attention is, " What is it for ? " Thus to 
take the case already spoken of — we see certain ani- 
mals with teeth of a peculiar shape ; we see one of 
them using these teeth to tear the flesh of some animal 
which it has just caught, and devouring that flesh as 
food. The adaptation of the teeth to the end for which 
we see them being used, is sucli that we have no doubt 
that such was their design or Final Cause. 

1146. One case is enough. It seems to let us into 
One case suffi- tlic sccrcts of Naturc — the counsels of the 

thfebeiief"^^^'' Creator. We feel as though we knew why 
He had so made the animal ; and we predicate that 
mode of life of all animals having the same Formal 
property, as a general fact. We hold it as a physical 



in.] METHODS OF PEOOF AND REFUTATION. — SECT. V. 315 

certainty — but not as an absolute certainty. For not 
only may the nature or formal properties change in 
some respects, but influences may exist in some cases 
which will turn individuals and even whole species 
from the course of nature. 

1147. There are sometimes cases of individual de- 
formity. Most of the species of domesticated cases of de- 
animals have been changed by domestica- f<^^^^»^y- 
tion ; and some of them so much that it is now diffi- 
cult to ascertain precisely what they were in their 
undomesticated state. Man, we see was made for vera- 
city, benevolence, and virtue ; but his history shows 
that there has been a very general departure from what 
his nature shows that he was intended for. 

1148. The Fundamental Principle of this doctrine 
of Final Causes is, that whatever exists in 

,1-1 . p ^-^ , * 1 f* 1 Fundamental 

the domam oi JN ature exists lor some end or Principles in 

T .11 » 1 1 ' this doctrine. 

purpose, and consequently where its consti- 
tution and use indicates a purpose, we infer that that 
was the purpose designed, and consequently the law 
of its being which was imposed upon it by its Creator, 

1149. Now taking this Principle for our Major 
Premise and we have : 

That for which any thing in ISTature was evidently 
designed it will accomplish. 

Canine teeth were evidently designed for a carni- 
vorous habit of life. 

Therefore, Animals with canine teeth will always 
be carnivorous. 

1150. Hence as Induction always implies that 
whatever is or occurs, is or occurs for some induction ai- 
purpose or design ; so it implies also a rn^^%ntinj^ent 
Wisdom which comprehends all things and creator, 
events, and never errs — and a Power which can ac- 
complish all that that Wisdom can design. 

1151. In the domain of Nature it is immaterial, so 
far as the result is concerned, whether we ^ physical Mat- 
begin with the constitution of the object as ffom ^Mo7ai'^ pw" 
seen in its Formal Properties, or with the l^^^^l to the Final 



316 LOGIC. PART II. [chap. 

Final Cause as seen in its Modal — the result is in each 
ease and alike the same. But with man it is not so. 
We see from his constitution that he was designed for 
But not in Mo- vlrtuc. But wc scc much in his Modal pro- 
^^^' perties — that is, in his thoughts, feelings, 

and actions — that is not in accordance with the Final 
Cause of his being ; much which therefore we pro- 
nounce to be wrong, or at least abnormal. 

1152. So too in Nature, there are abnormal cases 
in which we cannot infer from the individual the de- 
Abnormai cases slgu or law of thc modc of life which his 
in Nature. spccics was intended to pursue. If we should 
find a man, without legs from his birth, it would not 
answer to infer from him that all men were designed 
merely to sit or to crawl, and that walking is a viola- 
tion of the law of man's being. Such anomalies occur 
in nearly all species of being. And Hugh Miller*^ 
has suggested that there may be, and that in fact there 
are reasons for believing that there are, in Nature 
whole species which have been degraded from their idea 
or normal condition. Of such he thinks that serpents, 
venomous insects, and insects with stings, are exam- 
ples. His remark would include all those which have 
means of injury to other beings not necessary as either 
means of defence or of taking their prey. 

1153. The Argument from Examples, or a Fact as 
an Example, is evidently but an induction from a sin- 
Facts as Ex- gl^ inducted fact ; as when we argue from 

ampies. -j-j^^ f^^j^ ^]^^^ Astrouomy was opposed by 

religious bigotry, when it first began to be cultivated 
by the Christian Philosophers in the Middle Ages, 
that Geology will be in like manner opposed as sub- 
versive of the Christian faith. 

1154. It is evident that the particulars denoted by 
the terms " Astronomy '^'^ and '^ Geology ^^ in this case, 

There must be i^^^^^st liavc a rescmblancc, consisting of iden- 
liinf ^Sf'com^ tity in the properties on which the compari- 
parison. g^j^ ^^ argumcut is based. And in estimat- 

♦ Old Red Sandstone, final Chapter. 



in.] METHODS OF PROOF AND REFUTATION. — SECT. V. 317 

ing the force of an Argument of this kind, the first step 
in each case is to consider whether there really is that 
resemblance or identity or not. 

1155. But we are at present concerned only with 
the Method and its proper force. The Argument stated 
in brief is this : 

Astronomy when first introduced was opposed as 
adverse to religion. 

.-. Geology when first introduced will be opposed 
as adverse to religion. 

1156. This is manifestly an Enthymeme, in which 
the Minor Premise is suppressed. 

AisP, 
.-. G is P. 
We may complete the Formula by aflirming A of G. 
Thus, 

AisP, 

G is A, 
.-. G is P ; 
that is, by saying that " Geology is Astronomy." But 
that is not true. Astronomy and Geology are not iden- 
tical ; nor is Astronomy a species within which Geo- 
logy is included. All we can say, and all that the 
Argument from Example means to say, is that they are 
alike. But as this does not affirm either identity of 
spheres, or include the one in the other, no inference 
can be drawn by means of such a proposition in a 
categorical Syllogism. 

1157. The Force of the Argument from Facts as 
Examples, therefore, must be sought in, the The inference 
point of resemblance, considered as the fhaffd^entitT" 
Formal Properties of a Species. 

Thus Astronomy, when first introduced, was a new 
science, contradicting some of the prevailing theologi- 
cal opinions. 

But Astronomy was opposed by the religious when 
first introduced, hecause it contradicted, &c. 

Therefore all sciences which contradict the preva- 
lent theological notions, will be opposed when first 
introduced. 



318 LOGIC. — ^PAET n. [chap. 

1158. With this Conclusion for a Major Premise, 
we introduce " Geology is a new science, contra- 
dicting the prevalent theological notions ; " and we 
have the conclusion, therefore " Geology will be op- 
posed," &c. 

1159. It will be seen that in form this is but an 
Example an luduction from a sin2;le Example as an in- 

Induction from T,if»i i ii ir» li 

a single Fact. Quctcd lact, aud as such depends tor whatever 
value it may have either as a Method of Investigation 
or of Proof, upon the principles and laws of Induction, 
and the extent to which it fulfils them."^ 

1160. This Method is seldom, if ever, spoken of in 
Seldom called commou usc of language as an Argument 

Example except /. -r-^ i j. i_ '^ • T t j^ 

in Moral Matter. Irom Jixample, cxccpt when it is applied to 
Moral Matter. In that case the value of the Method 
is much less, since there is no such uniformity of 
Causes and Laws in Moral as in Physical Matter. 

* Whately, in his Rhetoric, Part. I. Chap. U. § 6, has given the Ar- 
gument from Example in a form which is, perhaps, more striking than that 
in the text, as follows : 

Astronomy was decried at its first I Geology is likely to be decried, 
introduction as adverse to religion : | &c. : 



Every science is likely to be decried at its first introduction as adverse to 
rehgion. 

But this Major Premise is untrue, and can be saved only by the Modal, 
inserted above : " Every science which contradicts the, prevalent religious 
opinimis — " In this^jase the Modal not only limits the subject to an included 
species, but is also in fact assigning the Cause, and we might therefore have 
the Causal Argument. 

Astronomy was decried because it opposed the prevalent religious 
opinions. 

Geology opposes the prevalent religious opinions. 
.'. Geology will be decried. 

And in fact the inference of a General Principle from a single fact as 
Example, or many, as inducted particulars, must always be limited in one 
of these two ways — namely, either to instances of the same kind only, or to 
instances in which the same cause is at work upon matter which is essen- 
tially the same. 



m.] METHODS OF PROOF AND KEFUTATION. SECT. V. 319 

1161. The Induction of Facts by way of Example, 
is but a loose and vague way of reasoning. Argument from 
and is seldom satisfactory. For in all con- dom"'^s\tisfac- 
tingent matter, that there are exceptions to ^^'^• 

all rules is proverbial ; and the Argument from Exam- 
ple often has the appearance, and is in danger of the 
reality, of being based upon the exceptions rather than 
upon the individual facts coming under the Rule. Thus 
if one should attempt to prove from Examples of dreams 
coming to pass, that dreams are to be regarded as 
generally prophetic, or signs of what is to take place, 
he would most manifestly be arguing from the exception 
to the general rule. Yet Examples of what he is trying 
to prove can undoubtedly be produced. Nor in fact 
is there any proposition in Contingent Matter, however 
absurd, which may not find some Minor Premise, 
which by way of Example, will connect it in the fulfil- 
ment of Formula with some indisputable Major Pre- 
mise, and thus prove it to be true with all the force of 
which the Argument from Example is capable. 

1162. Two affirmative Premises in the 2d Figure 
constitute an Analogy between their sub- Analogy how 

jeCtS. As, constituted. 

A is B, 
CisB. 

A and C must therefore be analogous, or identical 
in the Matter of the conception B. 

1163. But if we take that Matter as a Formal Pro- 
perty, and then predicate of A or C some 

other Modal Property in a compound Causal, perty'°tlken'S 
assigning B as its Cause, we may predicate 
that Property also in an Argument from Analogy of 
the other of those subjects. Thus, 
AisC, 
B is C. 
But A is X hecause it is C, 
.-. B is X. 

1164. Thus Bishop Butler argues from the analogy 
between the death of man and the chrysalis state of 



320 LOGIC. — PAET n. [chap. 

the worm, that the soul of man is immortal. The 
Bishop Butler's chiysalis and the man have but few points 
argument. ^^ common. Yet some such points or pro- 
perties they have — and the analogy is in this case 
somewhat remote ; and in consequence requires much 
greater scrutiny, and can never in fact produce the 
same degree of certainty as the closer analogies. 

1165. This Argument put into Form would stand 
thus : 

Man has a principle of life. 

The worm has a principle of life. 

The worm lives through an apparent death, hecause 
compkfeT'"' it has the principle of life. 

Therefore man will live through the appearance 
of death at the dissolution of his body. 

1166. Or without the Causal we may have the 
probiernatic Problematic Conclusion, (which is in all 
Conclusion. cascs Valid of the Affirmative Premises in 
the 2d Figure,) 

Therefore man may live through the apparent ex- 
tinction of his being at the death of his body. 

1167. There is sometimes a presumption, but no- 
thing more, arising from the fact that two individuals 

Analogy in "which arc known to agree in many points as 
aiwayr'f'safe ^ commou Esscutia, will agree in a certain 
ence"to''ani'iogy othcr poiut lu regard to which it is not yet 
in others. kuowu whcthcr they agree or not. But 
arguments based on such supposed analogies are of but 
little value. Thus a man and a horse agree in a vast 
number of points of the animal economy, but still they 
may disagree in regard to that property by which a 
certain plant is food for one and a poison for the other. 
The probability is against any such proposition on the 
ground of general analogy, but still it is only a proba- 
bility ; and the proposition may be true, as we know 
that it is true in a vast number of instances. 

1168. The reason for the inferiority of tlie Argument 
. Why Analogy from Aualofi-y to an Induction, results as will 

18 inferior to i /> *-'•' .i . t x» j_i i 

Induction. be seen irom the madequacy oi the class- 



III.] METHODS OF PKOOF AND REFUTATION. SECT. V. 321 

conceptions which we have in our own minds — an 
inadequacy which Induction and Analysis properly 
used are all the while removing, and the removal of 
which converts the Induction into Demonstrative 
Sciences just as fast as it progresses. 

1169. There is another use of Analogy which is of 
great value, and which we ought not to fail Analogy as a 
to notice in this place. It consists in remov- Sowng amecl- 
ing antecedent objections and improbabili- dent objections. 
ties, in interposing objections to too hasty inductions, 
or inferences from inductions too broad for the inducted 
facts. 

1170. Any inference which is too broad for the 
facts — that is, an inference including a Genus in what way. 
comprehending several species from facts gathered 
from one species alone, must comprehend the facts of 
the other species also as being necessarily analogous 
to the extent of their common Essentia. If, therefore, 
such analogous facts can be adduced, which are not in 
accordance with the inference, they are an answer to it. 
This is the case with Butler's Analogy. It refutes the 
Major Premise of the sceptic, by substituting a new 
Minor Term, ''the Chrysalis" for "Man;" and with 
the same Middle and Major Terms, the Bishop deduces 
a Conclusion which is contradictory to an indisputable 
fact."^ But as the new Minor Premise cannot be dis- 
puted, the Major Premise is proved thereby to be 
untrue, and consequently the inference from it to the 
death of the soul of man, is invalid. 

* The Infidel had inferred from the appearance, that man's being ter- 
minated at the death of the body. His argument was that : 

Man appears to end his being at death. 

Therefore his being does end, and the immortality of the sonl is but a, 
dream. 

But the Bishop says, Your principle, Major Premise, proves too much ; 
for the worm when it goes into the chrysal^ state, appears to die, as evi- 
dently as man, and yet the worm comes out a butterfly. Man niay^ there- 
fore, notwithstanding the appearance, come out of the apparent death 
a purely spiritual being, with powers and faculties which he does not now 
possess. 

14* 



322 LOGIC. — ^PAKT n. [chap. 

1171. In the same way the antecedent objection to 
a miraculous revelation of the will of God in Christian- 
Removes also ityj IS answered by the fact that there has 

j^e"ctlon1;o'Re?e- bccn an intcrposition at the creation of man ; 
jation. ^^^ ^f there has been one such interposition, 

there can be no antecedent presumption against an- 
other's being made when there is sufficient occasion 
for it. 

1172. Both Testimony and Circumstances are to be 
Testimony and re^rded bv Los^ic as Facts. The reality and 

Circumstances V /»i'1«t»i n i , t 

as Facts. valuc 01 which, individually and separately, 

are to be determined by principles which do not belong 
to the sphere of Logic. But the force of co7iGicrrence in 
testimony and in circumstances, is a fact which it 
becomes important to consider in this connection. 

1173. By Concurrence we understand such a con- 
concurrence. ncctiou bctwecn two or morc circumstances, 
or pieces of testimony, as that one did not cause 
the other ; nor does the one serve to explain and 
account for the reality of the other, except through or 
by means of the principle which they are adduced to 
j>rove. 

1174. Thus two witnesses testifying in the presence 
Of Testimony of cach otlicr. Or after an interview between 

concurrent and .■% .t ^ * a. j? ii ' i j^' it 

accumujated. tlicm ou the subjcct ot their testimony, could 
hardly give what would be fairly considered concurrent 
testimony. It would be accumulated testimony, and 
worth just as much additional force as the moral char- 
acter of the second witness, and his opportunity to 
know could give it. But the testimony of the second 
might be accounted for on the ground that he knew 
what was the testimony which the first had given or 
was about to give. It could be a case of concurrence, 
and have the force due to a concurrence only on condi- 
tion, that the two witnesses had had no opportunity of 
knowing what each other had testified, or were about 
to testify to. 

1175. And so of circumstances ; when one will ac- 
ci?ciXsSii"e8.^ count for the existence of others, there is no 



m.] METHODS OF PROOF AND REFUTATION. SECT. V. 323 

concurrence. It is merely an accumulation of circum- 
stances, and in fact of but little value. 

1176. This is the Method of Argument upon which, 
for the most part, the conclusions of the The sphere of 
Historian — that is, the series of statements ^^^"^®- 
which make up what he calls his history, depend. Such 
is the infirmity of human testimony — man's liability to 
error in perceiving — his susceptibility to the uncon- 
scious influences of prejudice and passion, m History. 
and worse than all his perverse inclination to mistake 
and misrepresent others, that the cautious student of 
history will seldom believe even the most explicit 
testimony of a single witness, imless there are other 
witnesses or material circumstances concurring with 
his statement. And if the influence of this concur- 
rence be against any man's testimony clearly, and with 
any very great force, we set it aside with the charitable 
judgment that it was a mistake of his. 

1177. In the criminal jurisdiction of our Courts 
also, concurrence of testimony, or Circum- 
stantial Evidence, as it is called, is for the cnminar jurfs- 
most part all that can be had. The criminal 

never surrounds his acts with witnesses who can testify 
to his guilt. On the contrary he seeks to be as far 
removed as possible from such means of convicting him 
of the crime. 

1178. Moreover, as showing the value of this kind 
of testimony, there are some crimes of which 

X ^ • ^ T ri t .' Concurrence 

a man cannot be convicted on the testimony superior to sin- 

r» . 1 .. * i:\ A 1 gle direct testl- 

01 a sms^le witness, without a stronsr concur- mony m some 

5^ • 1. I.* ^ • T • cases. 

rence oi circumstantial evidence, as perjury 
for instance ; and in many cases concurrence of cir- 
cumstances is suflBcient to destroy entirely the direct 
testimony of an individual witness. 



324 LOGIC. — PAKT n. [chap* 

SECTION VI. 

Of Progressive Approach, 

1179. There are certain Methods of Argument 
which, while from their nature thej are incapable of 

Occasion for establishing an absolute certainty, do never- 
grlssive^* Ap* theless answer a good practical purpose ; 
proach. r^j^(j f^p certain extraneous reasons are pre- 

ferred in some cases to Methods which could give a 
different kind or degree of certainty. There are other 
cases where absolute certainty is unattainable, though 
we may make some approach to it. All these Methods 
we call Methods of Progressive Approach ; of which 
there are several kinds. 

1180. (1) A posteriori efforts to prove an a pi^iori 
proposition. 

1181. Suppose we take for illustration the first law 
First case. of motiou — " A body in motion will continue 
Illustration. ^^ movc for evcr unless it be stopped by 
some force external to itself." 

This proposition contains terms and elements which 
can never be justified by any a posteriori Method. In 
the first place we can never remove all the 
proof ^° ilTade- cxtcmal forccs that act upon any body, so as 
term^s of the to scc it iu inotiou uninfiuenccd by any thing 
Proposition. external to itself. Always there will be some 
friction, some resistance of the atmosphere, &c. But 
in the second place if we could fulfil this condition, an 
observation or experiment could never extend through 
the time implied in the Proposition to be proved, "/or 
everP We might, if the first condition was fulfilled, see 
it move a long time — but " for ever" is not only some- 
what longer than any individual observer will live to 
test the matter ; but, even if that difficulty could be 
satisfactorily disposed of, the proof of the proposition 
by this method could not be completed until it would 
be too late to be of any practical utility. 



m.] METHODS OF PROOF AND REFUTATION. SECT. VI. 325 

1182. Our only resource, therefore, is to approach 
the conditions as nearly as possible. We ^e can only 
set a body in motion with a given amount fl^^'^'p^feno^/i 
of friction and retarding forces — it goes a °^^^"*- 
certain length of time. We start the same body, or 
another precisely like it, with less of friction, and it 
keeps moving much longer ; and the less there is to 
retard it, the longer it moves— and we infer that if it 
had nothing to retard it it would move for ever. 

1183. The Proposition can be proved a priori from 
the property of inertia, which is contained in ^ ^^^ be De- 
the class-conception of Matter as a material Kionstrated. 
property. 

1184.' But a posteriori we can prove only general 
truths, with the possibility of exceptions to 
them, while the absolute certainty of uni- proved" oni7 by 

\ , ,^ I'l j'i* 1' Demonstration. 

versal truths, which admit no exceptions, 
can be proved only a priori by Demonstration. 

1185. (2) A second modification of this Method is 
afibrded in the mathematical doctrine of ^he Doctrine 
limits. That is, "Whatever is true of any ^^ogreiTivl ap^ 
point indefinitely near to any limit, is true p^®^""^- 

at that limit." 

1186. Thus if we have the question of the quadra- 
ture of the circle. What is the ratio of the 
diameter to the circumference ? We can tureof the^ck- 
answer only by Progressive Approach. We 

can construct a polygon within the circle, whose sides 
are near to the circumference of the circles, but not 
coincident with it. We may then bisect the sides of that 
polygon, and so on, but the polygon can never become a 
circle. It can only approach it indefinitely near. So, 
too, the number that expresses the ratio of the radius to 
the circumference becomes a decimal 3.141, and extend- 
ing indefinitely, but it can never become complete. 

1181. Arguments from the force of Terms, from 
Testimony, from Concurrence, from Circum- cumulative 
stances, in fact Cumulative Arguments, and ^^,\^rnln\^f}^ 
Probable Arguments of all kinds, are but fr^|'c?hes. ^'^' 



326 LOGIC. — PAUT n. [chap. 

Progressive Approaches towards the absolute certainty 
of the truth of the Proposition which they aim to 
establish. A jury in criminal cases, for instance, is 
bound not to convict a criminal so long as there is a 
reasonable doubt left of his guilt. And yet the records 
of criminal jurisdiction furnish many instances in which 
persons have been convicted, who were afterwards 
found to have been entirely innocent. 

1188. In speaking of Arguments of this kind as 
Progressive Ap- but Progrcssivc Approachcs to certainty, we 
m^e^ satfsS must bc undcrstood to refer to their Logical 
mSistmtrve.^^' character rather than to their practical effect, 
in point of fact the mass of minds are sooner and easier 
persuaded by a Progressive Approach than T3y a De- 
monstration, even in those cases where a Demonstration 
is possible. It require^a peculiar mental constitution, 
or at least much practice, to be so familiar with the 
Method of Demonstration as to be fully under the in- 
fluence of its power. 

1189. And on the other hand, minds which are 
particularly accustomed to the Methods of Demonstra- 

Danger of de- tiou, or which are constitutionally peculiarly 
gl-esitve^ A?' susccptiblc to its forcc, not unfrequently ac- 
proach. quire a contempt for what is called moral 

reasoning, and a distrust of its conclusive force, which 
is entirely unjustifiable. And it is, perhaps, one of 
the most difficult branches of practical Ethics, to deter- 
mine where the force of a Progressive Approach be- 
comes a sufficient ground for the responsibility of 
action. 



SECTION vn. 

Of the Argumentum ad Ignorantiam. 

1190. This Argument consists in proving that a 
Argumentum givcu Propositiou is truc, bccausc we know 
tiam. ^^"**^^'^' of no reason why it should not be true, or 
why the truth- should be otherwise. 



in.] METHODS OF PROOF AND REFUTATION. SECT. VH. 327 

1191. An instance of this occurs where we should 
least of all expect it, in Herschel's Discourse on the 
Study of Natural Philosophy. He says that lUustration. 
on the old principle, " that Nature abhors a vacuum," 
as accounting for the rising of the mercury in a Baro- 
meter, and such like phenomena, " We know of no 
reason why Nature should not abhor the vacuum as 
much on a high mountain as in the plain below." 
Therefore the Barometer ought to stand as high on a 
mountain as in the plain below. This of course as- 
sumes that if there was any reason for its being other- 
wise, he or we should know it ; or which is the same 
thing, that we know all the reasons for whatever phe- 
nomena may come before our minds. 

1192. Now there are undoubtedly cases in which 
one's is:norance of any fact or phenomena, 

^ ,. iii.i?*i. 'J Ig-norance of a 

IS a presumption at least oi its non-existence, fact or princi- 
Thus an alleged fact in any science of which a proof'of^^^ts 
none of those most familiar with the science °^'^'^^^*^^- 
had any knowledge, would be looked upon with great 
suspicion. And so universally just in proportion to 
one's opportunity to know, is his ignorance a ground 
or principle of proof of the non-reality of the alleged 
fact. 

1193. The Ad Ignorantiam labors not only under 
the disadvantages of Negative Testimony, and of Posi- 
tive Testimony to a Negative Proposition (858-863), 
but also under peculiar disadvantag-es of its 

-T7\ 1 i T ,1 • Value increases 

own. Jbor what man adequately conceives with our know- 
and knows, is an indefinitely small amount 
when compared to the infinitum of the knowable ; and 
the value of the Argumentum ad Ignorantiam increases 
from nothing up towards certainty, only as our know- 
ledge advances from total ignorance up towards omnis- 
cience. 

1194. There are some cases, however, in which this 
element enters pretty largely into our Methods of In- 
vestigation and Argument. In investigating use in investj- 
Causes, for instance, both Final and Efdcient, ^^^^°- ^^^««- 



328 LOGIC. — ^PAET n. [chap. 

so strong is the belief in their reality, that we often 
affirm the causality of a particular Antecedent or Mode, 
not because we can see any connection between the 
facts, but simply because we can see no other fact of 
which to affirm it. We can see no connection, for 
instance, between the resin and the kind of electricity 
that it excites. But Induction having established the 
invariable antecedence, we affirm a causality simply 
because we believe that there is a cause, and we do 
not know of any thing else that could have produced 
the observed phenomena, except the resinous sub- 
stances. 

1195. Such reasoning can hardly be said to be 
based upon any general principle which comprehends 

wantofprin- ^^L^ facts of the casc ; or in more exact terms, 
cipie. ^j^j principle, the statement of which fur- 

nishes a Middle Term, as a means of proving the Pre- 
dicate of the Subject in the Conclusion. 

SECTION vm. 
Of Refutation, 

1196. Refutation supposes a foregoing proposition 
already asserted or assented to, which it is desirable 

to disprove. As this foreeroing* proposition 

Refutation sup- ini • •.•.••i 

poses a conciu- cau narcllv be an axiom or intuitive luds:- 

sion of a tore- i-iii it i*^.^ 

going Argu- mcut, it must be regarded as a conclusion 
^^^ ' to a course of reasoning, or at least as resting 

on Premises or grounds, which must in some way be 
removed before we can expect those who have adopted 
the conclusion to give it up, or justify ourselves in 
dissenting from it. 

1197. In cases where there has been an Ignoratio 
Elenchi^ or the proof of a Proposition which is not 

gnoratioaRe- ^0 the purposc, wc havc uo occasiou to show 
futation. ^\^^^ ^]^g conclusion is untrue, by any method. 

It is enough to show that it is not to the purpose. This 
is not in fact so much a refutation of the Argument or 



m.] METHODS OF PKOOF AND REFUTATION. — SECT. IX. 329 

Conclusion, as the rescuing our cause from the effects 
of a false and improper attack. 

1198. Setting this case aside, therefore, as not 
strictly belonging to Methods of Refutation, we may 
divide all our Methods into three classes : — Three Methods. 
(1) the Direct ; (2) the Indirect ; (3) Personal Eefuta- 
tions. 

SECTION IX. 

Of Direct Refutation, 

1199. The first form of Direct Refutation to be con- 
sidered, is that in which we prove the contra- First Method, 
dictory of the PTOj>osition^ which may have been af- 
firmed without regard to any Premises or means of 
Proof which may have been given to prove its truth. 

1200. No Proposition and its contradictory can be 
true at the same time. If now we have any universal pro- 
Universal Proposition asserted, we can refute tS'^by ^Exce^p- 
it directly if we can find what is called an *'**"^' 
Exception — that is, a fact included in the sphere of its 
Subject, with which the Predicate of the Proposition 
cannot be connected by a Copula in the same quality 
as in the original Proposition. If that Proposition was 
affirmative, its Predicate must be denied of the Excep- 
tion ; or if negative, it must be affirmed of it. Thus 
if I say that all the men in a given company are sit- 
ting down, the Proposition would be refuted if one 
could show that there was so much as one exception, 
one individual that was not sitting down. 

1201. The mere inability to affirm the Predicate 
could hardly be regarded as a refutation. a caution. 
It would be a piece of mere negative testimony (see 860). 

1202. In all such cases the appeal is always to 
some of the primary means of investigation. Exceptions 
which, because they are primary, are both ^ow proved, 
investigation and proof (1040). 

1203. We must remember that Individual judgments 
always precede Universal or General judgments, and 



830 LOGIC. — PAKT n. [chap. 

that general judgments are based upon the individual."^ 
And by no principle can the general judg- 
judgmems"first mcut bc made more certain, than the least 
certain of the individual judgments compre- 
hended in it ; as the chain can never be any stronger 
than its weakest link. Hence the assertion of an 
exception to any Universal Proposition is but an ap- 
peal to the primary judgments ; and of course, there- 
fore, it must have a greater degree of certainty than 
the Universal Proposition itself. 

1204:. An Exception, however, never refutes a 

Exceptions do mcrc oenerol Proposition, since in all con- 
not retute Ge- . . *1 . . »,* • i • • i 

nerai Proposi- tmgcut matter it IS a recognized principle 
uSiversaL °" ^ that all sucli admit of exceptions. " Excej)- 
tlo probat regulam^'^ has come to be an axiom. f But 
an Exception is a refutation to a Universal Proposition. 
It destroys its Universality, and therefore its Formal 
character. Of course it is immaterial whether the 
Proposition was affirmative or negative, so far as the 
effect of the Exception is concerned. 

1205. But if the Proposition to be refuted be Par- 
Refutation of ticular rather than Universal, then of course 
Proposition."^' it cau bc rcfutcd only by the Proof of its 
contradictory Universal. And this can be proved in 
one of two ways only : (1) first by an a priori demon- 
stration in necessary matter ; or (2) by an actual in- 
spection of all the individuals included in the sphere 
of the Logical Whole ; a part of which constitutes the 
subject of the Particular judgment which we wish to 
refute.:}: 

* The Individual judgment is always first in point of time, and if we 
proceed from that hy Induction we get a General judgment ; but if we 
evolve the Predicate from the necessary matter of the conception of the 
subject, our judgment becomes a Necessary one. 

t Of course it is not the Exception that proves the mle, strictly speak- 
ing : but the fact that it has been noticed as an exception., proves that the 
general Proposition, to which it is contradictory, has been recognized as a 
rule which is true in general. 

X In the first case we obtain a judgment, which is Universal, ex neces- 
sitate rei ; in the second it is only Universal, de facto — as in fact there is no 
necessity that it should be so or always remain so. 



in.] METHODS OF PROOF AND EEFUTATION. SECT. IX. 331 

1206. But there may be many cases in which nei- 
ther of these modes of direct refutation are Refutation of 
practicable, where we can have no a priori ^pt a^wTys' pos" 
demonstration — nor yet submit the indivi- ^^^^®' 
duals included within the sphere of the subject to the 
test of observation and experiment. 

1207. In all such cases we may release ourselves 
fi'om the obligation to assent to a Conclusion 

hy refuting the Reasoning. This we accom- thol^o" Direct 
plish not by disproving the Conclusion, but 
by showing that it is not proved by the Premises ; we 
show in fact from the Premises themselves without 
referring to any matter not contained in them, that the 
Conclusion is invalid, and ought not to have been 
drawn from those Premises. It may be true as a Pro- 
position, but is not proved as a Conclusion. 

1208. This may be done in four ways : (1) in the 
first place we may have a simple Non seqici- Nonseqmtur. 
tur^ as in all cases of Fault or Fallacy in Form. In 
this case the Premise may be true and the Conclusion 
true, and yet no connection between them ; or the 
Premise may be true and the Conclusion false. Thus 
if any of the five Canons (477) be violated, we have a 
simple I^on sequitur. 

1209. So, also, if in Conditionals we deny the Ante- 
cedent to destroy the Consequent (682), or j^^^w sequuur 
from the denial of the Consequent infer the ind^^^'oiirunc- 
contrary and not the contradictory merely ^^''^^• 

of the Antecedent. Or if in Disjunctives, we apply 
the Modus jpoiiente tollens (710), where the excluded 
Middle is produced by the opposition of alternate 
rather than coordinate species or parts. In short any 
Fault or Fallacy in Form will give a N'on sequitur. 
Hence it is always a sufficient refutation to point out 
such a fault. 

1210. (2) In the second place we may have a Sequi- 
tur per Fallaciam — using the word Fallacy in sequuer per 
its strictest sense — as indicating some decep- ^«'^«c^«^«- 
tive use of a Formula, where the Premises, each taken 



332 LOGIC. — PAKT n. [chap. 

by itself is true, and the conditions and require- 
ments of the Formula are fulfilled. Of these it will be 
seen (Part I. Chap. lY. Sec. 3,) that there are five : 
(1) Ambiguous Middle ; (2) Division ; (3) Composi- 
tion ; (4) Accidents ; (5) Quid. 

1211. Any one of these Fallacies of course destroys 
the validity of an Argument ; and although the Con- 

.The conciu- clusiou may still be true, we are no longer 
true notwith^ bouud to reccivc it as a Conclusion after 
Faikc?^ ^ such a Fallacy has been pointed out in the 
process by which one has arrived at it. 

1212. (3) In the third case we may have a Sequitur 
per non veram^ in which case there is neither fault in 

Sequitur per Form uor Fallacy in the use of matter, but 
nonveram. simply the assumptiou of Premises, one or 
more of which are not true. 

1213. This will be seen occurs in the case of Won 
causa pro causa^ as stated in Part I. (738), together 

Cases of Peri- "with thc assumptiou of Sequence where there 
tioPrincipii. ig none, non-exclusion of Middle, &c., &c. 
In all these cases a Proposition is assumed as true, 
which is not so. And whether it be expressly stated 
or implied as the suppressed Premise of an Enthy- 
meme, the Sequence of a Conditional, &c., it is equally 
mischievous; and needs to be distinctly evolved if it 
were not expressly stated. 

1214. It thus becomes a Proposition, which we shall 
The False Pre- uccd to disprovc — uulcss its falsitv be ob- 

mise will need . 'ii . p rm • ^ n 

disproof. vious without any proof. Ihis can be done 

of course only by proving the contradictory of the False 
Premise. 

1215. (4) But finally, we may have a Fault in Me- 
thod, or a misapplication of Method to Matter ; as if 

Fault in Me. ^c sliould attempt to apply Demonstration 
thod. ^Q contingent matter, and determine realities 

in being from our conceptions, stated as definitions. 
This was the great fault that prevailed among the 
students of the Natural Sciences from Aristotle down 
to Bacon. 



ni.] METHODS OF PEOOF AND REFUTATION. — SECT. X. 333 

1216. But in modern times we have a tendency to 
the opposite error. One writer ^ has attempted to ap- 
ply Liduction to the religious history of the voiney's Fault. 
world, and to prove the falsity of Christianity from the 
fact, that all religions except that contained in the 
Scriptures have been delusions. 



SECTION X. 
Of Indirect Refutation. 

1217. This consists in proving a Proposition untrue, 
by showing that it contains or comprehends indirect Refu- 
that which is false. ^^^•^°- 

1218. In the first place we may show a Proposition 
to be false by evolving from it, hy Immediate bj immediate 
Inference^ an untruth. Thus, one writer says in^'^'ence. 
that the human souls are propagated by '' decision ; " 
and the context shows that by " decision " he means 
the cutting ofi" of a part. But " decision " or division 
implies extension, and extension is a property of mat- 
ter and not of spirit. 

1219. In the second place we may refute one's 
reasonins; by what is called the Reductio ad 

^7 7Tj1' 'ij Refutation by 

Aosurdum. In this process we introduce a Reductio ad 
other matter, which is either admitted as '^^ "^' 
true, or which admits of proof beyond further question, 
and combines this new matter with that part of which 
was given before, which we wish to show to be false. 

1220. This Method is often spoken of as the process 
of showing that one's "Principles" or "argu- popular names 
ment proves too much." Thus the infidel's ^^^^he Method, 
argument, that the apparent death of the body implies 
the death of the soul and the cessation of existence, as 
Bishop Butler shows in his Analogy, " proves too 
much." It proves that the larvae of the Metabolians 
die when they go into the chrysalis state ; whereas 

* See Voiney's Ruins, or Meditations among the Ruins of Empires. 



334 LOGIC. — PAKT n. [chap. 

they do not die but only change their mode of exist- 
ence. 

1221. Now if any general Proposition, that is, a 
Proposition with a general term for a subject be true. 

Fundamental ^^s Prcdicatc must bc truc of every species 
fnSt^Refu^ included in the genus denoted by the sub- 
tation. JQQj^^ jf ii^QYi we can discover a species, of 

which the subject of that general Proposition can be 
predicated, while its Predicate cannot, the general 
Proposition itself must be untrue. 

1222. Thus to recur to Bishop Butler's argument 
Illustration. again. The infidel had asserted that the soul 
dies with the body — the assertion was based on the 
appearance of death — and hence implied the Major 
Premise, that " in all cases of an apparent death of the 
body, there is a total cessation of the existence of the 
individual." — Using this Major Premise, we may com- 
plete the Formula thus : 

Whenever the body dies there is a termination of 
the individual existence. 

The body dies in what we call the death of man. 

.*. In what we call the death of man there is a ter- 
mination of the individual existence. 

But says Bishop Butler there is a death of the body 
in the larvae of Metabolian insects. Using this for a 
Minor Premise to the Major Premise just given, and 
we have for Conclusion : 

.'. There is a termination of the individual existence 
of each Metabolian when it goes into the chrysalis 
state. 

This Conclusion, however, is confessedly untrue, 
and yet the Major Premise is the same as the infidel 
had used ; the Minor Premise is indeed difterent, but 
then it is a Proposition that no one can dispute.* Hence 
the Major Premise, common to both Conclusions, must 
be untrue. 

1223. By this we do not mean to say that the Pro- 
The disproved positiou had uo element of truth in it, or 

1 a^tTyTrlTe? ^ that tliis Ecductio has shown that the Predi- 



ni,] METHODS OF PEOOF AKD REFUTATION. SECT. X. 335 

cate is not true of any individuals included in the sub- 
ject ; but only that inasmuch as the Proj)osition is not 
true of all, we cannot admit it to be true of any, until 
it is modified by some modal which shall give either 
the Differentia of an included species of which it may 
always be affirmed, or expressive of a term or a condi- 
tion in which it may be affirmed of any one of them 
generally. And until this has been done by the infidel 
the refutation is complete. 

1224. The Indirect Methods of Disproof as well as 
the Indirect Method of Proof imply that there mdirect Me- 
is more than one way of knowing the truth •^"p'Jy a^D^ect 
of the Proposition which it is sought to dis- f^^^""^ condn. 
prove. Otherwise there would be no means ^^°"' 

of disproving. Thus, as we have seen, we may dis- 
prove a Proposition by proving directly its contra- 
dictory. This gives us two methods to the same Pro- 
position, since from any Proposition to its contradictory 
is an immediate inference. 

1225. Or again, we may disprove a Proposition as 
a Premise by the reductio ad absurdum. 

But this implies that we have some other the ^R^SictiS 

,^ ^ n • ji i /^ 1 • ad Absurdum. 

means or metnod oi proving that (Jonclusion 
or its contradictory, as the case may be. Otherwise 
we should not knoAv which of the two Conclusions was 
right. We cannot pronounce our Proposition to be 
absurd or false, until we have ascertained that it is 
contradictory to another which we know to be true. 
Affirmative judgments are antecedent in point of time 
to the Negative, and the test of a theory or Method is 
that it gives results in accordance with what we know 
to be true, independent of the Method or theory in all 
those cases of which we know any thing, except by 
means of the theory or MetLud itself. 

1226. The value of the Method will of course de- 
pend upon the certainty of the newly intro- .The Refuta- 
duced Premise or Matter, and of course is upon the'^cer- 
worth nothing unless that Premise be more new Mauer. 
certain than the common Premise which it seeks to 
redargue. 



336 LOGIC. — PART n. [chap. 

1227. What is called the Argumentum ah Absnrdo 
The Argumen- is merely th 6 inference from the Absurdity 

turn ab Abnur- jy j_t r^ i • .t . i t *:. 

do- 01 the (Jonclusion, that one or the other of 

the Premises, or both of them must be untrue. This 
can seldom be of any further use than a mere appeal 
to prejudice, since one is not likely to announce an 
absurd opinion without some force of Premises to sup- 
port it which may need a Eefutation. 



SECTION XI. 
Of Personal Refutations, 

1228. There are certain Methods of Eefutation, 
which, while they have no conclusive force of a general 
Personal Refu- charactcr, arc often of great rhetorical effi- 
tations. ciency in putting a stop to further contro- 
versy. These I have called Personal Arguments, 

1229. (1) The Argumentum ad Hominem consists 
Argumentum ^^^ appealing to a man's acts, or previous de- 

adHomimm. claratious, or avowed principles, as being 
inconsistent with the position he is at present main- 
taining. 

1230. The ad hominem proves nothing^ categori- 
what it proves, cally. Tlic opiuion of the Eespondent is used 
as a Premise against himself; It may eflectually annoy 
or even answer him ; but it can prove nothing more 
than that su^h and such is his opinion, or results from 
his opinion. The Conclusion can have no more truth 
than the subjective Premise or personal opinion of the 
person to whom the Argument is addressed. 

1231. (2) The Argumentum ad Verecundiam is an 
Argwmentmn appeal to the opiuiou of an authority which 

dfaw. ^^'■^^"^' the person against whom the argument is 
used is bound to respect and follow, on the score of 
modesty. 

1232. This argument also can hardly be said to 
Its force. prove any thing categorically. It is used 
and very well serves to embarrass an antagonist. 



m.] METHODS OF PROOF AND EEFUTATION. — SECT. XI. 337 

Beyond this it has but little force. It gives for a Pre- 
mise the opinion of the individual or authority cited, 
and the Conclusion can have no force except what 
results from the respect due to that authority ; a 
force which may have far greater moral than logical 
weight. 

1233. The Argumentum ad Invidiam as it is some- 
times called, is really no argument at all. Argumentum 
It consists in appeals to the passions, preju- ^a invidiam. 
dices, or feelings of people, for the purpose of exciting 
emotions unfavorable either to a cause or the person of 
him who advocates it. However effective this may be 
in a rhetorical point of view, it accomplishes nothing 
logically ; and proves, if it proves any thing, only that 
those who resort to this mode of argument are better 
skilled in Rhetoric than in reasoning, and know more 
of the Formulae of Billingsgate than of Logic. 



15 



338 Loaio. — PABT n. [chap. 



CHAPTEE IV. 

METHODS OF INSTRUCTION AND CEITICISM. 



SECTION L 

Classification of Sciences. 

1234. It may not be inappropriate to give a Classi- 
fication of the Branches of Human Knowledge before 
proceeding with the appropriate topics of this Chapter. 
Such a classification has been already anticipated in 
some measure, and seems very generally to have been 
considered as belonging to this part of Philosophy. 

1235. We have already referred to the early divi- 
sion of human knowledge into three branches : Physics, 

Early ciassi- Ethics, aud Logic (5). But a slight advance 
be?om"s inTcfe" ^^ sciencc, howcvcr, rendered this classi- 
quate. ficatioH inadequate and unsatisfactory. It 

must however be, to some extent, the basis of all divi- 
sions. The first department. Physics, including all 
branches of knowledge that have for subject-matter 
material objects in the concrete ; Logic, including all 
branches that treat of the intellect, and are based upon 
the elements furnished by it, the realities of truth, and 
the a priori conceptions ; and Ethics, including all that 
relate to man as having a destiny to accomplish, im- 
plying society, religion, and the state with its institu- 
tions and vested rights, as of Property, &c., as a means 
of accomplishing that destiny. 



IV.] METHODS OF mSTRUCTION AND CKITICISM. SECT. I. 339 

1236. It would not be worth the while to follow 
the history of these classifications minutely if we had 
time. One or two of the classifications, how- Aristotie'8 
ever, it may be well to notice. Aristotle classification, 
divided all knowledge in the first place into two coordi- 
nate parts, the Ir)imediate^ in which we learn every thing 
in particulars and each by itself {ra ku^' efcacrra)^ and 
the Mediate^ in which we acquire a knowledge of univer- 
sals (ra Ara^ o\ov). From the Immediate in his theory, 
we deduce by means of Logic the knowledge of the 
Mediate. Hence Logic is the instrument or organ of 
all science, so far as its form is concerned. "With 
another view he divided all knowledge into Philosophy 
and History. Philosophy Ije divided into Speculative 
and Practical. The Speculative becomes Physics or 
Mathematics^ or what is afterwards called Metajphysics^ 
according as it advances in abstraction ; and relatively 
to its end^ it is divided into Physics, Cosmology, Psycho- 
logy, and Theology. Practical Philosophy includes 
Ethics, Politics, and Economy. 

1237. In the Scholastic Philosophy of the Middle 
Ages we have the division into the Trivium and the 
QuADRrvauM ; the first including Grammar^ scholastic 
Rhetoric^ and Logic ; and the latter includ- classification. 
ing Arithmetic^ Miisic^ Oeometry^ and Astronomy, 
They were described in these mnemonic lines : 

" Gram, loquitur ; DiA. verba docet ; Rhe. verba ministrat ; 
Mus. canit ; An. numerat ; Ge. ponderat ; As. colit astra." 

1238. These seven sciences constituted what in the 
University distribution was called the Faculty of Arts. 
And besides these were three others : Divi- ^.^ ^^.^ ^.^ 
nity^ Law^ and Medicine, The first is tribTtfon'of the 
regarded as including whatever concerns 
Religion and its duties ; the second whatever relates to 
the State and its administration of aflairs ; and the 
third was understood to include the Physical Sciences 
generally. 

1239. Bacon proposed a new classification, dividing 



340 LOGIC. TART H. [CHAP. 

all Sciences into three classes, as they refer to either 
Memory^ Imagination^ or Reason, But this resulted 
Bacon's ciassi- ^^ grcat coufusiou, as there is scarcely any 
fication. branch of knowledge in which all these 

faculties are not called into use ; and as has been re- 
marked, '' his classification would put Boswell's Life of 
Johnson in the same class with the labors of Cuvier, 
and the researches of Hunter." Botany and Zoology 
were classed with Metaphysics, and Painting and Mu- 
sic among the " artes volujAuarias^^'^ were ranked with 
Cookery and Cosmetics. 

1240. Locke gave a much more sensible classifica- 
ficauon!' '^^'''' tion, as follows : 

( Economies, ( Logic, 

2. Peactica < Politics, 3. Semeiotica < Rhetoric, 

( Ethics. ( Grammar. 

1241. DuoALD Stewart believed a classification of 
the Sciences impossible, at least in his day. Colekidge 

Stewart and attempted it as a basis for the Encyclopedicc 
Coleridge. Metvopolitana^ which was constructed on 
his plan. But as a confession of failure, he was obliged 
to give an '-'- and so forth'^'' at the end; or rather a 
chapter of " Miscellanies ^^'^ which could not be in- 
cluded in any part of his division. This reminds us 
of the Treatise of Smalgruenius, entitled " De Omni- 
hus Rebus^'^ with a supplement, " De Quibusdam 
AliisP ^ 

1242. Ampere, however, elaborated a classification 
which is perhaps complete enough. But it is too com- 

Amp^re's pHcatcd. Colcridgc had failed by so classi- 
ciassification. lying, as to make his exceptions too nume- 
rous. Ampere made his parts too numerous, and had 
to create names and sciences which were never before 
heard of. His division does not recognize those names 



m.] METHODS OF INSTRUCTION AND CKITICISM. SECT. I. 341 

and divisions whicli are already in use. N^or is there 
the remotest probability that the progressive develop- 
ment of Science will take the form and divisions that 
he has pointed out. He makes one hundred and 
twenty-eight sciences in the last subdivision, or third 
order, as he calls it — and thirty-two of the first order. 
He first divides into two kingdoms : — Cosmological, 
including (1) Mathematics ; (2) Physics ; (3) Natural 
Sciences ; (4) Medical Sciences ; — and Noological 
Sciences, including (1) Philosophies ; (2) Pialegma- 
tics ; (3) Ethnological Sciences ; (4) Political Sciences, 
124:3. CoMPTE has given a classification also in his 
Positive Philosophy, as follows : compte's cias- 

■*■ *^ sification. 

(Astronomy, ct>v. • i 

I. Inoeganio ^Physics, K Oega:n^o J^^JSioiogy, 

(Chemistry, ] Sociology; 

and then, as preceding and implied in all, he gives 
Mathematics or the Science of Numbers. 

1244. This classification, as will be seen, does not 
include many of those which have thus far always been 
regarded as distinct sciences. Nor is the division suffi- 
ciently minute to be of much service. His Theory 
of Knowledge and his Philosophy are too hopelessly 
bad to allow of any useful classification being based 
upon it. 

1245. In the following classification which I shall 
give, I divide first into three classes with ^ ^^w one 
reference to the end in view ; and in the sub- p^^opo^^d. 
divisions I have followed the received divisions and 
names. Each class naturally divides itself into two 
departments, diff*ering in the first class both in the 
starting-point and in the Method. In the second class 
they differ in the starting-point only ; and in the third 
class the two departments differ chiefiy in the object 
in view — the one producing objects of Beauty and the 
other objects of Utility. The Sciences in the depart- 
ments in the first class are necessary to those in the 
second class, and those in the second are necessary to 
the third. 



342 



LOGIC. — ^PAET n. 



[chap. 



Class I. — ^Theoretical, 
including those Sciences the object of which is " to 



department I, 
^xact Sciences ^ (purely physical), based upon 



of facts 



Primary 
Phenomena * 



^in the Atmosphere . 
ahove the Atmosphere 

r in the structure and Nat. 
History of the Earth 
on the surface of the 
Earth . 
in the .analysis and combination of 

the simple Elements 
in the form and Nat. History of 

Solids on the Earth's surface . 
in the structure of living bodies . 
of the internal functions of Life 
in the structure and varieties of 

Vegetable Life 
in the varieties and habits of Ani- 
mal Life . . . , 
in the varieties and migrations of 
Men . , . , . 

as exhibited in Con- 



of mind 



sciousness 
in the external acts of 
man 



Meteoeology. 
oueanogeaphy. 

. Geology. 

, Geogeaphy, 

. Ohemistey. 

. Mixeealogy, 

, Anatomy, 

. Physiology. 

. Botany. 

. Zoology. 

, Ethnology. 

. Psychology. 

. HiSTOEY.t 



* Beginning first with the facts of Observation, we have what are the 
strictly Indnctive Sciences. I have called them the Exact Sciences^ in ac- 
cordance with the popular usage ; not because they are any more exact 
than others, but because (if any reason can be given) they depend upon and 
requhe the greatest exactness of Observation— they depend upon Observa- 
tion and Testimony. 

t History, properly understood, will of course include a knowledge of 
ancient Geography, the Languages of ancient as well as foreign nations of 
the present day. It will also imply a knowledge of the systems of religion 
and modes of worship that have prevailed, and the progress that man has 
made in the Arts and Sciences, in Philosophy and Literature, 



IV.] METHODS OF INSTKrCTION AND CEITIOISM. — SECT. I. 34:3 



DEPARTMENT H. 



Pure Sciences^ (purely metaphysical), based upon 



Primary 
Conceptions 



of unity . 

of forms in Space 



. Arithmetic. 
. Geometry. 
^ Constant 
Quantities . Algebra. 
Fluxional 
Quantities . Calculus. 



of combination I represent- 
of Symbols [ ing 

of the meeting of lines and planes 
in a point Trigonometry. 

of visible representation of Equa- 
tions .... AlNalytic Geometry. 

of the combination of Conceptions in 

Syllogisms Analytics. 

of Matter as modifying processes of 
Thougbt Method. 

of the conditions and forms of Know- 
ledge t Ontology. J 



* Then in the next place I start with that other great coordinate in all 
knowledge, the elements of thought which exist nowhere in the reality of 
being, hut which the Reason itself furnishes ; and where all possible things 
are assumed as real, or rather the distinction between the possible and the 
real entirely disappears. Even the varieties of Method are based rather 
upon the varieties of Matter conceived as possible, than upon the results 
of experience in matter, although as the two coincide there is no necessity 
of observing the distinction in discussing Methods. 

t By Ontology we mean the science of being, and it should include the 
discussion of the necessary law or forms of thought under which we know 
and believe whatever is supposed to exist out of the individual mind of the 
thinker. It wiU thus be found to furnish the fundamental and axiomatic 
principles of all the Exact Sciences, and in fact give to them their form or 
their Formal Cause. 

X The Sciences in this Department are purely instrumental and valu^ 
able ag Means and Helps to the construction of the Materials given in the 
preceding Department into the Sciences in the next two Departments, and 
in applying them to use as in the Departments in the third Class. 

The six first named, Arithmetic, Geometry^ Algebra^ Calculus^ Trigonometry, 
and Analytic Geometry, constitute the Department of Mathematics ; while 
of the other three, two, Analytics and Method, constitute Logic ; and the 
three together, with one from the first Department, Psychology, constitute 
what is ordinarily called Metaphysics. 



84:4: 



LOGIC. — ^PAET II. 



[chap. 



Class II. — ^Peactical,* 
including Sciences the object of which is " to doP 



DEPARTMENT I. 

Mixed Sciences f based upon the Conception of 



Matter 

and 

Motion 



in solid bodies 



\ on the Earth 

( in the Heavens 

. V .1 ^ at rest 

in liquids jj^^^^j^^ . . . 

in gaseous masses 

in bodies as affecting jjj^ ^f^^^l^ 



. Mechanics. 

asteoxomy. 

Htdeostatios. 

Hydeaulics. 

Pneumatics. 

. Acoustics. 

. Optics. 



DEPARTMENT IL 

Ethical Sciences % based on the conception of 



Man 

and 

Action 



in relation to the Idea of the Good . 
as exercising authority in temporal 

affairs 

as under Divine Providence 
(the State 



as under Au- 



<the Church 



thority I ^ Revelation from God 



. Ethics. 

Polity. 

N'at. Religion. 

jueispeudence. 

EccL. Polity. 

Rev. Religion. 



* The sciences in the second class are those which develope and state 
the laws of motion and of action. I have called them Practical because their 
End is Action ; they all assume more or less of the results of the Theoreti- 
cal, or sciences included in the first class. They proceed from the results 
there ohtained hy demonstration to the evolution of rules or laws. 

f These sciences I have called Mixed, since although the laws of Mat- 
ter are determined from the conception of its nature and constitution alone, 
yet the law itself is in point of fact for the most part first ascertained by 
observation. But it is soon found to be implied in our conceptions, (1) of 
Matter (as opposed to Mind) ; (2) of Force (as opposed to Motive) ; and 
(3) of Motion (as opposed to Thought). 

X In the second Department we consider the laws which man ought to 
obey. These are derived from a consideration of man as ho is (Psycliology 
and Physiology), and of the destiny, which, by his voluntary activity, he 
ought to attain. But as this destiny implies as a means of its accomplish- 
ment Society or the Family, and the State, that is, a society having sov- 
ereignty over individual men, and a Providence or Moral Governor of the 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. I. 345 

Class III. — Productive,^ 
including the Sciences the object of which is " to created 

DEPARTMENT I. 

The Fine Arts^ or Sciences which guide the expen- 
diture of labor, directed to the production of 

in the Soil . . • . . Gardening. 
in the construction of Edifices . Architectuee. 
in solid representations of Life . Sculpture. 

The Beautiful \ in perspective representations by 

Color Painting. 

in the combination of Sounds . . . Musio. 
^ in the use of Language . . . Poetry. 

world, to whom man is accountable, and whose final approbation is an 
essential part of his destiny, we evolve by Analysis and Demonstration from 
these conceptions Society, State, and Providence — the rules which man 
ought to obey. Hence Ethics, Polity, and Natural Religion, are based upon 
Reason alone. And the reaHzation of Religion implies a Church having 
authority in matters of faith. Hence we have, besides the authority of God 
over us, the two others. State and Church, which we find that He has 
recognized and sanctioned as guides* and authority, each within its appro- 
priate sphere, and we have both Jurisprudence and Ecclesiastical Polity as 
rules of action within certain limits. 

* In the third class I have included all those sciences the end of which 
is to aid man in the accomplishment of results out of himself, and have 
divided them into two classes, the Beautiful and the Useful. The Subjects 
included in this Class are more commonly called Arts than Sciences. They 
are, however. Sciences of the Arts ; that is, branches of knowledge which teach 
how to produce results, the production of which is called Art. Art is dis- 
tinguished from mere Instinct by this fact — namely, that it is guided by a 
scientific comprehension of its principles and processes, whereas Instinct has 
no such comprehension. 

t I have not regarded the Methods of Esthetics as properly coming 
wi^in the province of Logic. They are determined rather hy the Suscep- 
tibihty than the Reason. Their ultimate Facts are only experimental ; we 
can only refer to the fact that a beautiful object does excite the Emotions, 
which we call the emotions of Beauty ; and we judge an object to be beau- 
tiful because it does excite such emotions. We cannot prove tliat it ought 
to do so. We can discover no necessity in the nature of the case for its 
exciting such emotions. Its judgments in fact are all Relative, while Logic 
deals with the Absolute alone. 

16* 



346 



LOGIC. — PART n. 



[chap. 



DEPARTMENT IL 



Useful Arts^ or Sciences which guide the expen- 
diture of labor, directed to the production of 



in the Soil ..... Ageiotjlttjee. 
in objects beneath the Soil . . METALLrEGY. 
in the manufacture of the raw ma- 
terial Technology. 

f written Lan- 



in multiplying 
the products 
of mind 



expressed I guage . Typogeaphy. 
in I works of the 
The Useful -! ""^ ^^^"^"^ J I Fine Arts . Engeaving. 
in the increase of value by Ex- 
change OOMMEEOE. 

in tbe promotion of Health . . Medicine. 

in the expression of thought by 

Language Ehetoeio. 

in promoting pecuniary prosperity . Polit. Economy. 
in promoting the National Defence . . Wae. 

1246. Of course all the above-named or described 
Sciences admit of being greatly subdivided. In fact 
Each Science ^^J author has thc right to take any part of 
TabiS admits ^"^1 ^"^^ Scicncc and treat it as a Science by 
for subdivision, itsclf, if hc chooscs to do SO. This is, in fact, 
making a subdivision of some part of the division of 
Science as it previously existed. In this way the 
names on our Catalogue of Sciences become more 
numerous, and may in fact extend beyond any known 
or conceivable limit. I have not thought it worth 
while, however, to follow the subdivisions already 
made, any further than they are given in the preced- 
ing three Tables and the Notes accompanying them. 

* But in the second part of this Class we have the Useful Arts. They 
take the results of the General Facts obtained by the Sciences in the First 
Department of the first Class, and the Laws obtained in the corresponding 
Department of the second Class, and by Deduction apply them to the results 
which minister to man's physical and temporal wants, as being subservient 
to the purposes of life ; which purpose again is the attainment of that End 
or Destiny for which his Creator placed him in this state of existence. 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. H. 347 

SECTION II. 

Of the Conveyance of Ideas from one Mind to another. 

1247. All Methods in so far as they belong to the 
Sphere of Logic, are determined by the Idea of the 
True. They aim merely to satisfy the demands of 
comprehension and conviction. But most, if not all, 
the Methods of Argument and Instruction 

come also within the Sphere of Rhetoric. Logfc and of 
They aim not only to convince, but also to 
please and to persuade ; and in Instruction especially, 
to save time and labor, and to facilitate the ease with 
which we remember what we have once learned. But 
the Methods of Rhetoric are determined by the Idea 
of the Useful. Its precepts are valuable only because 
they are useful — useful for pleasing and persuading — 
useful for the perspicuity of statement — lucidness of 
illustration or impressing upon the mind a sense of the 
importance of what is communicated. 

1248. It is obvious, therefore, that by far the largest, 
though by no means the most important, Methods of 
part of what properly belongs to any ade- strucSSS/" "^' 
quate discussion of the Methods of Instruction, must 
come within the appropriate sphere of Rhetoric. I 
shall, therefore, make but a very short Chapter on the 
Method of Instruction in this place. 

1249. By Instruction we mean not merely the 
communication of the knowledge which we instruction and 
have obtained. Our attention is much more construction. 
completely j&xed upon the means of Constricction^ or 
the putting it into a system, and so arranging the parts 
as that they may best fulfil the conditions of a thorough 
comprehension of the general subject by those who are 
unacquainted with it. 

1250. I regard it as a controlling fact in regard to 
Methods of Instruction, that a conception conceptioni 
cannot be conveyed or transferred, as a municate^d'^'^ai 
whole^ from one mind to another. Each one ^^^'e^- 



348 LOGIC. — TAUT n. [chap. 

must be formed de novo in each mind. No one can 
convey his sensation to another ; we can describe them 
to those beings, and those only who have had sensa- 
tions of the same species — the sensation of color, for 
instance, which I have when I look at the object before 
me, I cannot communicate to any other person. If 
he can see, I can describe it to him so that he can form 
a conception of it. But if he be blind, he cannot con- 
ceive of a sensation of color, nor can one be conveyed 
into his mind. 

1251. A judgment may be conveyed from one mind 
Judgments ^o auothcr, providcd both minds have the 

^^^- conceptions which constitute the matter of 

the judgment. Thus if I affirm that " gold is yellow,'' 
the person hearing me does not need to judge whether 
it is yellow or not, in order to understand my judg- 
ment, or the proposition affirming it — the proposition 
conveys the judgment to his mind, and he may then 
affirm or deny it as he pleases. 

1252. But a conception cannot be conveyed in that 
way or in any way. It is necessarily constructed by 

and within every mind in which it can exist 
may beTecaSed at all. Thus supposc I havc a couccption of 
known ^fo^r an au obiect, and use some word in an unknown 

unknown word. , i 'x^i^x J''i- j 

tongue to express it, that word is just as good 
m itself as any other, and just as good relatively to all 
who imderstand the language to which it belongs. 
But it has no power of itself to convey or suggest the 
conception. If the conception is one which has been 
already formed, and is in the mind of the person to 
whom I am speaking, all that I need to do is to 
define my word by giving its synonyme in the lan- 
guage which he uses. If I had used the word " caleb^'^ 
which is Hebrew, I have but to give the English 
word '^ dog^'^ and I have defined the word and re- 
called to his attention the conception which the two 
words are used to represent in their respective voca- 
bularies. 

1253. But suppose the conception be entirely new 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. IH. 349 

to the person addressed, no mere definition of the word 
by which I denote it will suffice. I must verbal pefini- 
give him first the Essentia of the object by convey'^concSp- 
referring it to the Proximate Genus, and *^®"^- 
then the Difi*erentia, which distinguishes it from the 
coordinate species in that Genus. And then further 
if it be an individual object, I must give some of the 
individual marks or inseparable accidents. 

1254. The person addressed then takes wp together 
(for that is the meaning of the word '' conceive ^^), all 
the matter which I have given and puts it ^he person ad- 
together in his own mind, as I gave it to stmctf the^coS- 
him, and he has the conception which I ^eption. 
had. But he has formed it anew in his own mind ; I 
gave him the material only. I defined my conception 
by an analysis of its matter, and he constructed his by 
a synthesis of the same matter. 

1255. But each of these elements into which I 
resolved my conception by analysis, and out of which 
he constructed his by synthesis, are also conceptions 
conceptions ; and if they are conceptions ISttufn"^ '""mo 
which he has not already formed, he is not J^?^® coS- 
prepared to synthesize out of the material ^^^°^* 
which I have given him. My Definition has not been 
sufficiently elementary, I must go back one step further 
and define the elements of which he has not yet formed 
a conception. 

SECTION ni. 
Of Definition and Description. 

1256. The predicating of any subject its Essentia 
and Differentia is what is called Definition. Definition. 
Thus if I say, " Mahomet was the man who founded 
the religion called iy his narae^'' I give first the Essen- 
tia — what he was — " a man ; " and secondly, ^y^gre d^je- 
the Differentia, which distinguishes him from ^**"^*- 

all other men " who founded the religion^'^ &c. By 
these words I have given an adequate definition. 



350 LOGic.-rPAET n. [chap. 

1257. But suppose I had omitted the Essentia, and 
Specific. Defi- Said, "he was the founder of the religion," 

quite.^ ^"^ ^' &C.5 this would be a specific definition ; but 
the question might still recur as to his Essentia, whe- 
ther he was " man," " angel," or " demon." In that 
case the definition would have been inadequate, inas- 
much as " founder of the religion," &c., may be the 
Differentia of Species in several different Proximate 
Genera, as " man," " angel," &c. 

1258. Or again, suppose I had merely said, " Ma- 
homet was a MAN of AraMaJ^ Here the Essentia 
Definitions of In- " mau " would bc satisfactory to give me a 
givi'^?hi%ndi"4- distinct conception, but the words '' of Ara- 
duai marks. bia," are no Differentia of an individual 
man, since there are many '' men of Arabia." The De- 
finition would be inadequate. It would not be definite. 
It would give the Essentia with the Differentia of the 
species, but no peculiar or distinguishing mark of the 
individual. 

1259. A Definition is either of a name or of the 
Definition of a couccptiou which we have of a thing, or of 

ce&° or^°of the thins: itself by means of its conception 

the thing. & J r 

or name. 

1260. When we define a name or a word, we ex- 
Definitionofa pl^in its meaning by other words having 

name. ^]^^ samc meaning. Thus we define (^iXea} 

in Greek and amo in Latin, by the word '' love " in 
English. We explain the name " sulphuric acid," by 
Verbal Defini- raying that it is the " oil of vitriol." This 
tions. -[g called a Yerbal Definition, as merely de- 

fining words. 

1261. A real Definition is one that defines the thing 
itself of which the conception is formed. But as we 

Real Defini- kuow the thing or subject-matter only by the 
tions. conception which we form of it, we can of 

course define it only by means of that conception. To 
define any thing, therefore, is to define or give by 
analysis the conception which we have of it. Our con- 
ception may be compared by this means with those 



IV.] METHODS OF INSTEUCTION AND CRITICISM. SECT. HI. 351 

which other persons have of the same object, and cor- 
rected, if found to be erroneous or inadequate, by means 
of theirs. This correction, however, implies that their 
means and opportunities of investigation have been 
superior to ours. 

1262. We may, however, sometimes enable another 
to form a conception of the thing itself, with- Descriptions 
out the intervention of any conception which llu\e^lTlo''l 
we may have formed of it ourselves. This ^^'^pt'ons. 

we do by a Deseription pointing to the place in which 
it is situated, the time when it occurs, or the circum- 
stances by which it is surrounded. In this case we 
simply refer to the sphere of its conception, and leave 
others to learn the matter for themselves by their own 
observations or investigation. 

1263. It has been very generally held that there 
are certain simple Ideas and ultimate elements in all 
conceptions which cannot be defined. And the reason 
given for the opinion is, that being simple or ultimate 
elements they can be divided or analyzed no farther. 

1264. But this is evidently a mistake. We do not 
analyze the object in our definition, but only ^ 

'^ .• /» '^ IVT J.' *^ No Concep- 

our eonceptton or %t, JNow a conception ex tion that can- 

. , . -s *^ • i " i? • 1 1 not be defined. 

'^;^ termim can never consist oi a simple ele- 
ment. It is the taking together of several properties as 
Essentia and Differentia into a Logical Whole which 
to the mind represents the object denoted by the term 
which represents the conception. We get a conception 
of an object only by its Essentia and Differentia. And 
here the conception, including these elments, can be 
analyzed and so defined."^ 

* We must remember that it will often happen that the Differentia of 
any object, or class of objects, as we form our conceptions of them, will not 
consist of properties which can be predicated of the objects considered solely 
and by themselves. They are rather relative properties. Thns we may predi- 
cate " hardness" of iron in and by itself ; but " magnetism" is but a relative 
property, since we could never know its reality except by the relation which 
the magnetic body sustains to others which are attracted by it vN^hile in that 
condition. So with " causality," and many of the other elements which 
enter into our conceptions ; they indicate rather the relations which the 
objects sustain to others, than any properties which are directly perceptible 
by themselves. 



352 LOGIC. — ^PAKT n. [chap. 

1265. The difficulty however is in us. It is often 
the case that we have a distinct conception without its 

Reasons why bciug definite in our own minds. We never 
trmes%Vbi?fo have analyzed it, and perhaps cannot analyze 
define. ||^ g^ ^g j^^ name each element of its matter, 

and say what precisely is its Essentia and what its 
Differentia. Thus I suppose all persons have a pretty 
distinct conception of an apjple. But I doubt if any 
one can give the Differentia of it so as precisely to 
draw the line between it and the^^ar for instance. 

1266. Again there are objects the definition of 
which is made difficult, and practically impossible in 

Want of gene- somc cascs, by our having no well known 
rai terms. Proximatc Gcuus to which to refer them as 
expressive of their Essentia. Thus Prof. Loomis, in his 
Geometry, in attempting to define a " straight line," 
says, ^' It is the shortest path between two points. ^'^ The 
Differentia, " shortest between two points," is fault- 
less. But the Essentia, " path," sounds strangely. A 
line is not a " path " in any sense in which we are 
accustomed to that word ; that is, a " geometrical line " 
does not belong to any genus which we are accustomed 
to denote by the word '^ path." 

1267. This is in fact a difficulty often met with. 
We may have the Differentia of a conception at our 

A frequent dif- commaud, but uot its Essentia. In all at- 
ficuity- tempts to define " consciousness^^ for exam- 

ple, the same difficulty is encountered. Shall we call 
it a " faculty," a " function," or simply a " state " of 
the mind ? 

1268. The usual resort in such cases of our inability 
to define that of which, however, we have a definite 

The usual re- ^^^ ^^ distiuct^ conccptiou, is to describc 
^^^^' the sphere by means of the Differentia, and 

leave the Geiius or Essentia undetermined. 

1269. But an adequate Definition defines its object 
bj^ referring it to its species and genus. Thus we say 

* It mtiy be well to remark that the Essentia makes a conceptian 
" dktlnct^^ the Differentia makes it " dejinite.^ 



rV.] METHODS OF mSTRUCTION AND CKITICISM. — SECT. IH. 353 

that " Iron is a metal of great malleability^ density^ 
and of a darkish gray color P When we say ^hat consti. 
it is a " metal," we refer it to the genus *^^a?e %efin1- 
" metals ; " and of course we may thereafter ^^**°- 
predicate of it all the Essentia of metals. By saying 
" it is of great malleability, density, and of a darkish 
gray color/' we refer it to each of the species whose 
Differentia are respectively " malleability," " density," 
and " gray color." 

1270. We are said to define a conception generally 
or qenerically. when we refer it to its ejenus, 

^,, . '^^ • ^ 7 ?? • /? 77 ^ 1 Generic Defi- 

as " man is an amrmil y specijicaUy^ when niuons sped- 
we give the Differentia of the species with- 
out the genus, as " man is rational^^^ or " a being with 
reason ; " accidentally^ when we give merely Accidental. 
some accidental property of the object ; phy- Physical. 
sically^ when we enumerate the physical parts, as 
" man has two hands, two feet, erect form ; " and 
metajphysically^ when we refer to the invi- Metaphysical. 
sible nature, as " man is a spiritual being, with reason, 
intellect, memory, conscience," &c.^ 

1271. In delining a Genus, as such, the Essentia 
only can be given.f But in defining a Species, both 
the Essentia and the Differentia must be 

T. ir»» TT»T Til "What Defini- 

given ; and m denning an Individual there tions can be 
must be added to the Essentia and Differ- ^^^^^' 
entia the peculiarities which distinguish the Individual 
defined from others of the same species. 

1272. But when a Definition fails to fulfil these 
conditions, as if in defining a Species, there inadequate De- 
is an omission of the Differentia ; or in defin- fi^itions. 
ing an Individual an omission of the peculiarities, the 
definition is inadequate. 

* What is sometimes called a Negative Definition, or defining negatively, 
is no definition of the subject at all. It consists merely in naming the Dif- 
ferentia of the coordinate species, and saying that they are not properties 
of, and do not belong to the Species which we are defining. 

f We may of course refer it to the next higher of the subaltern Genera, 
in which case it becomes a Species to be defined as such by the Essentia of 
its Proximate Genus and its own Differentia. 



854: LOGIC. PAET H. [CHAP. 

1273. Definition, therefore, always implies a classi- 
Definition im- fication of the thinp* defined, by referring: it 

plies Classificaw ..,/->, t r>( • tt • . 

tion. to its Uenus and fepecies. Hence it appears 

that we can cognize the Individual only through the 
Species. Each property which we ascribe to it or see 
that it possesses refers it to a class, whose Differentia 
is the property thus ascribed to the individual object. 

• 1274. One of the readiest and best illustrations of 
this principle is afforded in the conjugation of the verb. 

The conjuga^ The vcrb itsclf is the Genus, and its Essentia 
^0^0" ySTn tli^ meaning of the word in its most general 
iuustration. scusc. Tlic Spccics is«ithe voice, as active, 
passive, &c., whose Differentia is the mode of the 
action of the verb in reference to the agent and the 
object. Mood is the first sub-species, the Differentia 
of which is the mode of affirmation as declaring (In- 
dicative), representing it as possible, &c. The second 
sub-species is Tense, and its Differentia is the relation 
of the action to the time in which the word is used by 
the speaker. The next sub-species is " number," indi- 
eating as its Differentia whether the subject of the verb 
included one or more ; and the infima species is the 
^-person," limiting by its Differentia the subject still 
further, by showing whether the subject is the person 
speaking, the person spoken to, or some person spoken 
of. And the word itself, as it stands on the written 
page, or is heard in oral speech, is the individual. 

1275. It is very likely to happen that the terms used 
in anv Definition will also need to be defined. In this 
case the laws of Definition are the same as 
to defi^e^^a^De- bcforc ; wc dcfiuc by Essentia and Differentia 
still. Thus if I should define the palm as 
" an endogenous tree," &c., one might be wholly un- 
able to construct the conception, because he had not 
previously the conception for which " endoge^ious " 
stands. I should then be obliged to define that con- 
ception by giving its conception, as applied to plants — - 
GROWTH hy suGcesive additions to the inside. But sup- 
pose my definition were not yet sufficiently elementary, 



TV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. HI. 355 

and that he had no definite conception of '' growth," 
I should be obliged to define it as a species of the 
genus " increase," giving the Differentia which distin- 
guish it from the coordinate species — accretion^ (^99^0- 
meration^ &c. Or suppose the words " by successive 
additions to the inside," represented a conception not 
previously formed in the mind of the person addressed, 
I should have to explain or define them in the same 
way, either showing what an " addition " is, or the 
difference between the kind that is " to the inside," 
and that which is " to the outside," its coordinate. 

1276. Hence as each Definition may need a defini- 
tion of its terms, there must be a constant ultimate 
retrogression until we come to some ultimate conceptions. 
Conception, which is formed at the first sight of the ob- 
ject ; or to Description, pointing out the sphere of the 
object of which the conception is to be found. 

1277. A Description, therefore, does not furnish the 
material for the construction of a conception. ^ Description 
It merely informs us when, or where, or how fhe^Mluer^^fo? 
we may find it for ourselves. And the pro- a conception. 
cess of finding it is one of the original Methods of In- 
vestigation. It brings us back, therefore, to primary 
or elementary conceptions. 

1278. These primary or elemental conceptions of 
external objects are formed spontaneously, primary con, 
and of necessity are the perception of the taneouTandSSi 
external senses. And of invisible objects, ^^-^ary. 
such as geometrical figures, &c., they are formed by 
the Reason constructing them in the mind itself. Thus 
suppose I imagine a point moving from one position in 
space always at the same distance from another point, 
until it comes back to the place of its departure, I have 
formed the conception of a circle by constructing the 
circle itself. It is for Genus a figure in space, and for 
Differentia it has a circwmference every point of which is 
equally distant from one and the sajnejpoint within it. 

1279. But this Genus, '' figures in space," cannot 
be a "primary conception for us, since we never have 



356 LOGIC. — PAET n. [chap. 

the Differentia denoted by the words " in space^'^ ex- 
conceptions of ^cpt as a countcrpart to objects having shape 
tmth'^^'Sy °a ^11^ outline in the external world or in place. 
cepuSn of reli- I <3o not dcnj that the conception would be 
ities of being, posslblc without such obscrvation. That is 
a question of metaphysics with which we have nothing 
to do in this place. But as a fact, all mortals here on 
Earth, do not form conceptions of the invisible realities 
of truth, until after experience of the visible realities 
of being in the material world. 

SECTION IV. 

Of Natural and Artificial Classifications, 

1280. The conception of each individual object — for 
with the individual we always begin in actual expe- 
rience — is formed by means of the Essentia 

first formed up^- and Differentia. I see an obiect before me 

on the basis of i . -, . -,-, -, -, •^.z, -,- -n ., 

those made by wnicu IS ycllow anci rouud ; II 1 call it an 
" orange," I refer it to a conception already 
formed, and consequently this is not a primary one. It 
is, however, the point at which each of us v/ho live at 
the present day begin with the formation of our con- 
ceptions. We learn the names that have already been 
given to things, and base our classiifications and con- 
ceptions upon those that have been made before us. 

1281. The primary classifications are always of 
necessity very simple and unscientific. Tliey are based 

on some property immediately obvious to 

Primary classi- ,i i i t d c* 

fi.cations very thc scuscs, as coior, sliapc, oQor, (fee, lor 
simp e. their Essentia. The next step is a division of 

the Genera, using different colors, odors, shapes, &c., 
as Differentia. This classification is almost instanta- 
neous if not quite so, at the first instant when the mind 
is awakened to activity by the presence of material 
objects to our senses. 

1282. From these first and purely accidental j^rin- 
ciDles of classification, we pass on in our progress of 



IV.] METHODS OF INSTRUCTION AND CRITICISM. — SECT. IV. 357 

comprehension, at each step adopting as permanent 
and useful such as have been found so in some of them 
times past, and because they have been so S'^of kn^ 
found have received those common names ^"^^®- 
which constitute the basis of all languages, as " com- 
mon names." 

1283. But no sooner do we begin our scientific 
investigations than we find in most cases 

that a new classification becomes requisite, new^cSssIfica- 

. . n 'I x J-' tions. 

one requiring lor its construction a new 
analysis of the objects to be included in the classes. 

1284. Hence the distinction between natural and 
artificial, or scientific classifications. Natu- Distinction be- 
ral classifications are such as are formed at Inr^sdenSfii 
once instinctively and of necessity by the classifications. 
mind. They are based upon the more obvious and 
conspicuous properties of the objects, and denoted 
by such words as the common names of all languages. 
The scientific classifications, on the other hand, are 
such as are based upon less obvious properties, and are 
devised for the purpose of expediting Science. They 
are, for the most part, denoted by what are called the 
technical terms of a language or science. 

1285. The problem in all scientific classifications is 
to group together in one species those facts which have 
the g-reatest number of properties in com- 

^ J , T .r» ■"- ii . • The problem 

mon, and to classiiy on those properties in scientific 

1 . 1 1 1 T7^ 1 'j.1 ^ Classifications. 

which are regarded as J^ ormal with reference 
to those which are Modal. The fewer the classes 
therefore the better, provided that in reducing the 
number of classes we do not increase the exceptions to 
each, so as to make the aggregate of Species and Ex- 
ceptions greater than in sbme other classifications. 

1286. Thus to take an example from Ethnology. 
If we divide men into three coordinate classes, red, 
black, and white, not only are the Modal An illustration 
properties common to each species in classi- from Ethnology, 
fication few, but the exceptions to any statement that 
might be made concerning any one of the species are 



358 LOGIC. — PART n. [chap. 

very numerous. As the result of much investigatioiij 
it has been found that if we class them as woolly- 
headed, bearded, and beardless, the number of state- 
ments, including both the rules and the exceptions, 
requisite for a full treatise on the Natural History of 
Man, is greatly reduced. Of course, therefore, that 
natural history when thus presented, is much more 
easily and much more quickly learned, and longer 
remembered than when presented to the mind of the 
learner by means of any other classification. 

1287. To take another illustration. In Botany the 
primary classification of its objects was into Trees, 

Shrubs, and Plants. CiESALPiNus proposed 
from"the\isu)ry thc first scicutific classificatiou based on " the 
of Botany. number, position, and figure of organs," as 
" the flower, the seed receptacle, and the seeds ; " for 
the purpose, as he said, of " ranging them into bri- 
grades, regiments, and companies, like a well-ordered 
army." Soon after Bauhin undertook another and 
simpler classification. Ray proposed another ; and 
in 1687 TouENEFORT proposed to classify on " the regu- 
larity or irregularity of the flowers in form, and by 
the situation of the receptacle of the seeds below 
the calyx or within it." Then Lestnaeus appeared and 
classified by ■' the pistils and stamens of the flowers." 
And finally, we have the system of the Jussieus, based 
on " the number of the cotyledons and the structure 
of the seeds, and subordinate to this the insertion of the 
stamina, as over, about, or under the germen." 

1288. A primary object is undoubtedly to make the 
number of the species as small as practicable. And 

The limit to ^hc limit to this reduction, as has been said, 
ofVe'^number ^^ the uumbcr of ^xccptlous and al)normal 
Species. peculiarities which always increases with the 

reduction in the number of classes, so long as we ad- 
here to the same principle of classification. And that 
principle which will give us the smallest aggregate of 
species and of exceptions, is said to be the simplest or 
to simplify the classification the most. 



IV.] METHODS OF DTSTEUCTION AND CEITICISM.— SECT. IV. 359 

1289. Now wherever we begin in our instruction, 
whether with the most general subject, as in the Syn- 
thetic Method — or with the individual, as in ^^ must de- 
the Analytic, we must define our subject, fS?e to 'b?th 
and each subject as we pass along, by refer- ^cSL cia^ 
ring it to the natural and well-known classi- "fixations. 
fications. And if we have adopted a scientific classifi- 
cation, we need always to give the common one also, 
and explain ours by the difference between them. 
Thus a chemist would say, " chloride of sodium is 
the muriate of soda of the old classifications — the 
common salt of the common use. It consists of so 
many parts of sodium, so many of chlorine," &c., &c. 

1290. In the course of our classifications we shall 
sometimes encounter a phenomenon which similar Differ- 
we have not yet noticed — namely, the recur- tSt'^prixi^te 
rence of the same Differentia of Species in ^^nera. 
different Proximate Genera — these we may cfes^"""^"^ ®^^' 
call Recurring Species, 

1291. Thus in Mathematics we have " curved lines" 
and ^^ curved surfaces," in which the Genera ''lines" 
and " surfaces " comprehend Species, whose illustrated 
Differentia is "curved;^'' as " curved Ym^^^^'^ fi^s"" and ^ S 
and " curved surfaces." Again in Gram- Grammar, 
mar, in the conjugation and declension of the Yerb, 
we have three voices, for instance, Active, Passive, 
and Middle. Now taking these as Proximate Genera, 
we have in each of them the same Differentia of 
Mood, Infinitive Mood, &c. ; and the Differentia, that 
is, the signification and force of Mood is precisely the 
sanae in one voice as in the other, although modify- 
ing a different Essentia. So, also, each Mood has dif- 
ferent Tenses, as a Present, and Past, and a Future. 
The force or Differentia of Tense is precisely the same 
in one Mood as in the other. It is defined as deter- 
mining " the time at which the Yerb represents the act 
as taking place ; " the Present represents it as taking 
place at the time of speaking, whether in one Mood 
or mode of representing the action or another, and irre- 
spective of the Differentia of voice. 



360 LOGIC. — PABT n. [chap. 

SECTION V. 

Of the Division of the General Subject, 

1292. The subjects of which we treat have exten- 
sion in two different directions. Comprehension and 

Two kinds of Pretension. If we are treating a general 
sions"iS'I^Gene- subjcct, as Chcmistry, Mechanics, (fee, it has 
rai Subject. Comprehensivc Extension, and admits of 
course of division into subordinate parts. If we are 
treating of an individual subject, as the history of a 
nation, the biography of an individual, it has Proten- 
sive Extension only. 

1293. In this latter case there is no logical neces- 
sity for a division at all. A division is only a conve- 
nience, and one that is often of very great 

cessuy ?o?a d1- importaucc both to the writer and the reader. 
t'enslve ^Exten." And as it is ouc that is required and deter- 
mined rather by the idea of Utility than the 
idea of Truth, we will leave its discussion to the Ehe- 
toricians. 

1294. But in treating of a general subject a division 
becomes necessary, in consequence of the fact that 

much which it is necessary to say, may be 
Generaislibjea predicated of a part of the included indi- 
necessary. yid^al subjccts which cauuot bc predicated 
of the whole ; and much of some parts which cannot be 
predicated of others. 

1295. If the subject will admit of a division into 
coordinate parts, it is best to divide in that way. And 

Coordinate ^hcu thc dlvisiou is to be determined by the 
part preferable. \^^ already laid down for scientific classifi- 
cations ; namely, so divide as that the aggregate of the 
number of the parts and of the exceptions to the predi- 
cates affirmed of the parts, will be the smallest that the 
nature of the matter will allow. 

1296. The reason for this rule is the same as that 
given above. The instruction can be given in fewer 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VI. 361 

words, consequently in shorter time, is more easily and 
sooner understood and better remembered. Reason for the 
than when the mind is encumbered by a ^"'®- 
multiplicity either of subdivisions or of exceptions to 
the statements made for general. Each coordinate and 
each subordinate part, as well as each exceptional case 
or individual, becomes a separate and distinct subject of 
predication, which it takes as long to teach and requires 
as much, and often more, effort to remember than the 
most comprehensive statement in the whole science. 

1297. But there are cases in which no division into 
coordinate parts can be made unless it be a very clumsy 
one. Our present general subject (828), "Me- in some cases 
thod," as has been already said is such an ^jdin^fe'^pai^s 
one. Again, if one were treating of the i°apossibie. 
Literary Men of a nation, it would be impossible to 
make a coordinate division that would answer any 
good purpose. 

1298. In such cases we must divide into Alternate 
Species. As in the case just named, we might divide 
the Literary Men into Historians, Poets, 
Essayists, Philosophers, Naturalists, &c. AitirnatTspe 
This would be a useful division. But the 

same man might be distinguished in more than one of 
the classes named, as for instance, the English Southey 
as a poet and as a historian ; Coleridge, a poet and a phi- 
losopher ; Macaulay as a poet, historian, and essayist. 

1299. And with regard to the number of Alternate 
Parts into which the General Subject should The same mie 
be divided, the same rule holds as above : numbe? of an 

..Tini.T .. 1 c J. ternate as of 

it should be the minimum aggregate oi parts coordinate spe- 

1 . . cies> 

and exceptions. 



SECTION VI. 
Of the Order in the treatinent. 

1300. In the first acquisition of knowledge we are 
obliged to begin with the individual and concrete, and, 

10 



362 LOGIC. — PAST n. [chap. 

examining them one by one, we ascend to the general and 
the abstract. Thus the knowledge of human 
know wfurthe naturc is acquired by an acquaintance with 
individual men one after another, analyzing, 
abstracting, and omitting what is peculiar to each, and 
retaining as the matter of the conception to be ex- 
pressed by one general term " man^^^ all that is com- 
mon to all men. 

1301. So, too, in acquiring the knowledge of any 
We also learn particular or individual object, we may per- 

Properties one ■*■ . . , , . r» j i i a* 

by one. ccivc its propcrtics, many ot them at a time. 

But we have to learn or study them, property after 
property, one at a time. 

1302. Now in teaching others, which is instruction, 
we may pursue the same method ; beginning with the 

. individual and the concrete, and proceed to 
Methpd "^^iS the general and abstract. This is called the 
ng. Analytic Method of teaching. But it is gene- 
rally found tedious, uninteresting, and unsatisfactory. 
And it moreover requires an examination of each of 
the individuals separately and in detail, which is in 
some cases impossible on account of the number, and 
in others they are inaccessible. 

1303. Still, however, in some branches of science 
this method is preferable, and perhaps even indispen- 
sable. In Botany, in Chemistry, in Anatomy, 

In some cases -, ^ ^'^ • i*7 'ii I 

the only Me- auQ such likc scicnccs, which consist almost 
entirely of details, and in which there are 
comparatively but very few general principles as yet 
established, we must of course confine ourselves to 
teaching the facts as they are known, and as far as they 
are known. The Causes and Laws which determine 
those facts are as yet unknown to us, if not altogether 
beyond the reach of our faculties. 

1304. In the Analytic Method of Teaching, the 
subject of which we speak is, of course, an individual, 

Analytic Me- ^^^ ^^^ P^ss from oiic to auothcr as fast as 
the"* iSSufi we have predicated of each what we know 
Subject. ^f jj.^ Qj. ^^ least that portion of what we 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VI. 363 

know of it which our purpose requires us to com- 
municate. 

1305. But in the Synthetic Method we begin with 
the general subject which comprehends the The synthetic 
individuals. We predicate of it whatever ^e^hod. 
belongs to it as a general subject, then divide it into 
its coordinate parts, and those parts again into their 
subordinates, and so on until we come to the indi- 
viduals included in each part. 

1306. As each part is less comprehensive than its 
whole, and so on until we come to the indi- 
vidual, each part will have something to be quiS^s s^cili 
said of it which could not have been predi- ^^^ '''^^''^"' 
cated of its superior and comprehending part in any- 
previous sections, and which ought to be predicated 
before we proceed to its subordinates. 

1307. These two Methods differ much less in rela- 
tion to the fulfilment of the Logical condi- 
tions of Method than would appear at first the' ^Methods 
sight. There is but one way of forming a ""^ ^'^^** • 
conception of a subject, whether that subject be the 
general subject of our treatise or the special subject of 
any subordinate chapter, section, or paragraph, even 
down to the individual. In all cases we form, and 
must form, our conceptions by means of classification. 
By classification also, and by that only, can we com- 
municate our conceptions to others. In the Analytic 
Method we teach by means of the natural classifications 
which all make naturally and necessarily ; while in the 
Synthetic we teach by means of those scientific classifi- 
cations which are the results of reflection, and some 
degree at least of advance towards the maturity of 
Science.^ 

* For an illustration take the following. Suppose a writer treating of 
Zoology synthetically, he would begin by defining his general subject, 
" animals ; " giving its Essentia as " living beiags," its Differentia '* with 
material organizations, and living only on organic matter, either vegetable 
or animal." The first clause limiting against spiritual beings, angels, &c., 
and the second against the vegetable kingdom. He would then divide into 



364 LOGIC. — PART n. [chap. 

1308. Our conception of an object may be analyzed 
into its Essentia, Differentia, Accidents, Quantity or 

Comparison, Cause and Effects. This order 

Matter of Con- . t . n •, • . , * ,n 

ception divided IS uot lu ail its succcssivc stcps stTicUy uecss- 

with reference t^ • t ii > • i 

to the order of saTy , it IS, nowcver, the most convenient, 
commumca ion. r^]^^ conccptiou is complctcd by the two first, 
Essentia and Differentia, in all that is essential to its 
comjpleteness. The others are necessary to its adequacy, 

1309. The Essentia and Differentia give us all the 
matter which is necessary to enable us to form the 

conception of any object of thoue^ht. They 

The Essentia \ ,. i\ in i. ' j. xl 

and Differentia arc, thcreiore, all that is necessary to the 

alone necessary -y pji ,* c* iiii 

for the «2Jnor2 adcquacy 01 the conception tor all the pur- 
poses of a priori Methods of Investigation or 
Proof, as in the Analysis of a Conception, giving us 
the Matter of Analytic Judgments and in the Demon- 
stration of the reality of Implied Properties. 

1310. But our conception of an object is never ade- 
quate, nor can our Science be completed until we have 

ascertained by the Methods of Investigation 
Qimntity! ^lc\ thc Accldcuts — iucluding the separable and 

necessary to the . it :\ ^^ n\ i.* -r\' a 

Conception for inseparable — and the Continuous or Discrete 
Science. Quantity and its Protensive Eelation to its 

antecedents and consequents. 

1311. Comparison is by no means a necessary ele- 
ment in the formation of our conception of an object. 

It may serve instead of Quantity. Thus if 
v^^^'S^fyri^- the question be asked. How large are the 
Hottentots ? The answer may be definite 



cessary 



four " Departments," — Vertebrata, Articulata, Mollusca, and Radiata, each 
department into Classes, classes into Orders, orders into Genera, genera 
into Species, species into Varieties, and varieties (the infima species) into 
Individuals, describing each in its order ; and in describing the individual 
he would refer it to the species, and thereby in effect predicate of it all 
that had been said of each subaltern species or genera up to the highest. Its 
specific name would at once classify and describe all that for the most part 
we care to know of it. But in the Analytic Method he would begin with 
the first animal he might meet, He would have to begin with saying, 
*' this dog^^ " this ca^," " this wormy' &c.j as the case might be, in all cases, 
however, referring to the common and weU-kijown class-names of the indi- 
vidual he might be examining. 



IV.] METHODS OF INSTIiUCTION AND CRITICISM. SECT. VI. 365 

in Quantity — '^four feet and a half ; " (which, how- 
ever, is after all a comparison with the foot^ taken as a 
unity of measure,) or it may be hy comparison^ thus, 
" much less than the ordinary height of Europeans." 

1312. Or we may have the question of quantity as 
to the comprehensiveness of the sphere of the concep- 
tion. Thus in describing a class, we say it Quantity of 
is a " large " or a " small " one. Or possi- h'ensive^neTof 
bly we give the precise number of indivi- ^^® sphere. 
duals included in it, especially if the number be small. 
Or again, we may give an idea of the quantity by 
comparison with another class, calling it larger or 
smaller than some other whose comprehensiveness is 
known. 

1313. There are many objects which we do not 
conceive of as Cause or as Effect. Thus in 
speaking of a Geometrical Figure, we should fect^not always 
not be likely to conceive of it as an effect '^"^"^'^ " 
whose cause is important to our knowledge ; nor yet 
should we think of it as a cause whose effects it could 
be important to investigate. Still, however, the con- 
ception of a triangle for example is an effect. It is the 
creation of mind, and it is a cause ; for it has stirred 
up all that mental activity which has produced the 
Sciences of Geometry and Trigonometry. 

1314. We come, therefore, to the Essentia and the 
Differentia as that which is always necessary Essentia and 
to a distinct and definite conception of any wSs'^"^necei- 
subject ; and which, therefore, must be Lo- ^^'^• 
gically first in all Methods of Instruction,'^ as well as 
in all constructions of systems and sciences. Without 
them there can be no conception of the subject, whe- 
ther general, special, or individual. 

* It is often advisable, for rhetorical reasons, not only to state the 
Differentia in such positive terms as connote the subject, but also to in- 
crease the distinctness of the outhne of our conception, by contrasting it 
with its coordinates speaking of their Differentia, thus fixing the attention 
upon them, and thus affirming that they do not belong to the class of objects 
of which we are speaking. This is sometimes caUed defining a subject by 
negatives, or negatively — that is, distinctly saying what it is not. 



366 LOGIC. — PART n. [chap. 

1315. By the Essentia we get a distinct concep- 
tion — the mind is assured of a reality, a substance, 

. ^.^^ since it has its Constitutive or Material Pro- 
Definite Con- pcrtics. But tlic conccption becomes 6?e/?- 
slntirind^Dif nite only by means of the Differentia. The 
Differentia distinguish it from others, conse- 
quently defines it, or fixes the limits within which it is 
a reality. 

We may, therefore, perhaps sum up the principles 
Principles of ^^ Ordcr lu thc Method of Instruction as 

Order. folloWS \ 

1316. (1) State first the general subject by its Es- 
First Principle, seutia and Differentia ; referring always to 
the natural classifications, even when we have occa- 
sion to use a scientific one."^ 

1317. (2) Divide it into coordinate parts or species, 
on the simplest principle at your command, and then 

Second prin- subdividc as far as the case may require, 
cipie. giving to each coordinate and subordinate 

part its Differentia, as we proceed to treat each of the 
parts in the order and degree of their subordination. 

1318. (3) Whatever subject we teach, whether the 
Third Principle, gcucral or either of the subordinate parts, 
define it first by Essentia and Differentia, that so tlie 
learner may know distinctly and definitely what we 
are treating of. 

1319. (4) The order in which the other topics, as 
Accidents, Quantity or Comparison, and Cause and 

Fourth Prin- Effcct OUght tO folloW, will dcpCud UpOU tllC 

cipie. YsvA we have in view. It is possible that 

Quantity is all that is desired. It other cases it will 
be wholly unimportant, and therefore deserving to 

* We are to remember that not all the Peculiar Properties of any class 
are to be regarded as its Differentia. The Differentia are only those pecu- 
liar properties which are most obvious and conspicuous. At least this is 
always so in the Natural Classifications. And much is added to tho per- 
spicuity and vividness with which instruction is communicated, by a suc- 
cessful tact in characterizing the subjects by those properties which, while 
they are peculiar and so determinate of species, are also conspicuous to the 
observation. 



1 



IV.] METHODS OF mSTRUCTION AND CRITICISM. SECT. VI. 367 

be omitted as surplusage. Again, the Cause or the 
Effect, either or both, may be the only thing demanded, 
or they may be a matter in which no interest is taken, 
and must be given or omitted accordingly. And so 
among the Accidental Properties — those must be 
selected which the object in view requires, remember- 
ing here as every where, that whatever is not condu- 
cive to the End, is to be rejected (764). This is one 
of the most fundamental principles of Method. 

1320. The mind is always impatient of any matter 
that is irrelevant to the End in view, and Themimiim- 
even of the intrusion of any piece of matter ^frunent'^mS- 
which is relevant, provided it be out of place '^'■• 

and comes in before something else that is necessary to 
its proper progress. Take the following example : — 
" The Coquallin was sent from America, by the name 
of the Orange-colored Squirrel, It is, however, not a 
squirrel. It is a beautiful animal, and very remark- 
able for its color, its belly being of a fine yellow, and 
its head as well as body varied with white, black, 
brown, and orange ; it covers its back with its tail, 
like the squirrel, but has not, like that animal, small 
brushes of hair at the tips of the ears : it never climbs 
up any trees, but dwells in the hollows and under the 
roots of trees, like the garden squirrel." 

1321. Now here after the assertion, " it is not a 
squirrel," the mind was expecting the Differentia be- 
tween it and the squirrel, whereas the author gives a 
series of propositions, which so far from being Differ- 
entia of natural species, may as well be applicable to 
the Squirrel as to the Coquallin. 

1322. Every body has observed the difference in 
the degree of ease with which they remember the writ- 
ings and instructions of different teachers. 

This is owing in a great measure to the per- memlfering de- 
fection of the Method of the Teacher. He t>d^n'''leach- 
has what is always necessary to successful 
teaching, a clear conception in his own mind of the 
subject and of the SDCcial end for which the instruction 



368 LOGIC. — PAET n. [chap. 

is at that time sought, and upon which therefore the 
interest in the subject itself depends. He, therefore, 
by the natural laws which govern the operation of his 
own mind, mentions the subject, referring it to a well 
known Proximate Genus, and then giving the most 
marked and distinguishing Differentia of its species. 
He carefully excludes all matter that is not pertinent 
and conducive to the end for which he is communicat- 
ing the instruction,'^ and finally selects and arranges 
whatever he is to predicate of his subject with reference 
to that end. 

1323. Rhetorically one of the first things for a 
teacher to do is to awaken an interest in his subject, 

by fixing: in the mind some End to be s-ained 
an interest in by thc iustructiou. Althougli this is a vio- 
lation of the principles of Logical Method, 
it is nevertheless so important to the rhetoric of in- 
struction, that it may well be placed in the rank of the 
highest importance. 

1324. The End must of course be sufficiently im- 
portant to awaken an interest in the subject itself, and 

Nature of the ^0 cxcitc that Interest to such a degree of 
^^^- intensity as to raise the mind to a high state 

of activity, and do away with the sense of tediousness 
which attends upon all aimless exertion. 

1325. If the mind were sufficiently capacious to 
comprehend all things — all the properties and bearings 

^ of any one subiect even — there would be 

Necessity for "^ 'I'lii iti i 

omission of many cases m wnicn there could be no need 
of such a principle of selection and omission 
as we have referred to. But the mind is not of suffi- 
cient comprehension to receive and retain all that we 
can learn or may desire to know. This fact is not per- 
haps very flattering. But it is well to have it distinctly 
understood and admitted. It may humble our pride 

* Quidquid praecipies, esto brevis : ut cito dicta 
Percipiant animi dociles, teneantque fideles. 
Omne supervacuum plcno de pcctore manat. 

HoR. De Are Poet 335. 



IV.] METHODS OF INSTRTJCTION AND CRITICISM. SECT. VH. 369 

somewhat, but it will make us wiser and teach us at 
an early day the necessity of economizing time and 
labor, and saving ourselves a vast amount of labor and 
toil, which would otherwise have been spent in vain. 

1326. It is no part of Logic to ascertain the various 
Ends for which instruction may be sought, and from 
which we may derive our interest in any subject. The 
End may be merely and purely the love of truth. It 
may be some immediate practical application which 
we wish to make of the knowledge w^e are seeking. 
But without such an End in view, but little will be 
sought and still less, effectually obtained. 

SECTION vn. 
Method of Logical Criticism. 

1327. Hitherto in our discussion of Formulae and 
Methods, we have supposed ourselves occupying a 
point of time anterior to construction ; and 
discussing the Formula and Principles by view^ occupied 
which to be guided in our work. But in ^^^^^"^'^• 
experience it is quite as often that we occupy a differ- 
ent position, and have to perform the part of the judge 
or the critic of that which has already been produced 
or constructed, or at least imagined for construction. 
We wish to criticise our own arguments and investiga- 
tions, theories and systems, before they go out to the 
world. And every where in Literature and Necessity for 
Science we meet with the like productions ^"^icism. 

of other minds which need to be thus examined and 
criticised, as a part of the process by which they can 
become our own or in any way profitable to us. 

1328. It is obvious that the Formulae and Principles 
must be precisely the same for Criticism as principles of 
for Construction. And so far as the Method ^^f^^^ tho^l 
of Criticism is determined by the Idea of the of construction. 
True, nothing further need be said than is contained in 
the precedinp- pages. It is immaterial in what way or 

16^ 



370 LOGIC. — PART n. [chap. 

order we apply these principles, if so be that we apply 
them and find the conformity or want of conformity to 
them in what comes under our notice. What we shall 
Its Methods, have to say further of the Method of Criti- 
cisms, therefore, will be determined by the Idea of the 
Useful, as giving the readiest and quickest way of ac- 
complishing the result. 

1329. In order to a successful and scientific Criti- 
cism, the first and indispensable step is to get an ade- 
quate idea or conception of the work to be 

Whole the starf- criticiscd, as a whole^ its structure and its 
ing-point. ^j^^^ j.^^ ^^ most cases we cannot get at 

the parts to form any conception of them, and criticise 
them without first analyzing the whole, that we may 
thereby discover what are its parts. But more than 
this an adequate conception of a part can never be 
formed without considering its relation to the whole 
The necessity ^s a constitucut part of it. Considered as a 
for it. whole and absolutely^ many a subject of our 

criticisms may be faultless, while yet it has no value 
or adaptation if considered relatively to its whole ; and 
vice versa^ parts that are faultless in reference to their 
comprehending wholes, are without comeliness and 
meaning, considered by themselves. 

1330. Wholes are never a mere accumulation or 
generalization of the parts. They are rather collective 

than 2:eneral. Many thins^s may be predi- 

The Whole not ^ a c^ r\ i-r ^^i.*^ j-^j 

a mere general catcQ 01 them which cauuot DC predicated 

Conception. r» pji ^-t tit 

01 any one oi the contained or comprehended 
parts. Much, for example, can be said of man as a 
living whole, which could not be predicated of any of 
the parts into which Anatomy, Chemistry, or even 
Metaphysical Analysis can resolve him. It is so of all 
wholes, and hence the necessity of examining and cri- 
ticising them as wholes over and above any examina- 
tion or criticism which we may give to their component 
parts. 

1331. This fault of judging of parts a^ wholes and 
not as parts merely, or in their relation to the whole, 



in.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VII. 371 

Whately has referred to the Fallacy of Division and 
Composition. It is, however, no Fallacy in Form. 
It is a Fault of Method originating in a want of com- 
prehensiveness of views. I have already quoted 
Whately's language in regard to it (749). To take his 
example : " The spendthrift compares his in- T^e spend- 
come with each particular item as a whole, *^"^''^ ^^'^^• 
and finds it small compared with what he has to ex- 
pend — five dollars for an evening's amusement out of 
an income of a thousand ! It is certainly inconsider- 
able. Such a sum cannot ruin any body. It is mere 
niggardliness not to afford it." But considered as a 
part of the annual expenditure it may, after all, be 
found to be just the sum and the item which will 
leave one in arrears at the end of his financial year. 
The same fault is often committed by persons in mak- 
ing their estimate of their own character and abilities. 
Not considering that one or two acts are sufficient in 
some cases to determine the character, they form quite 
a different estimate of themselves from that which their 
neighbors have formed. One or two acts of fraud, of 
intemperance, of intentional deception, destroy entirely 
one's character for honesty, temperance, and veracity. 
So, too, although it be true that " the best fail some- 
times," yet frequent failures to meet our engagements, 
or to perform the duties required or expected of us 
from our position, is ruinous to one's character for 
capacity or competency to the duties and responsibili- 
ties of his position.^ 

* It is often a successful trick of Sophistry to criticise what are called 
" the Points " of an Argument, as if they were wholes ; that is, Arguments 
each complete in itself, obstinately and artfully keeping out of view and out 
of consideration the fact that they are but parts of a cumulative whole. In 
this way the force of any Argument from circumstantial testimony or cumu- 
lative Argument of any kind, may he shown to have Httle or no force. 
The Method is no less absurd than would be the attempt to estimate the 
strength of an arch by ascertaining how much each stone taken separately 
would sustain, and then taking the aggregate as indicative of the strength 
of the whole arch ; when in ' fact more than one-half of the stones, per- 
haps, not only would not sustain any thing in their position, but need to be 
supported by those below them to keep them from falling. 



372 ' LOGIC. — PAET n. [chap. 

1332. What are to be regarded as wholes and what 
as parts, is determined by the choice of the mind from 

which they emanate ; and the same thing 
wiSt determin^ may bc regarded as a part or as a whole, just 

as in the nse which has been made of it 
in the case under consideration it was designed for a 
whole in itself, or to serve as a part to a larger whole 
and a means to an end not contained in itself. Thus 
a Treatise on the Evidences of Christianity may be 
planned and executed as a whole, to be complete in 
itself ; or it may be planned and written with reference 
to a particular end, to serve, for instance, as an intro- 
The same thing ductiou to a Trcatisc on Christian Ethics, or 
whoieTlome^ ^s SL part of a system of Theology. A volume 
times a Part. ^^^ Algebra may be designed to be complete 
as a whole, or only to serve as a part of a series on 
Mathematics ; and it will be modified in its plan and 
in its execution, according as it is to be a whole or a 
part, and will of course require to be criticised and 
judged by different rules, as it is to be regarded from 
the one or the other of these points of view. 

1333. Wholes are to be criticised chiefly with a 
view to the Principles of Method, the Methods by 

Parts to be wliich they are constructed. We may, 
considered^ in ^f coursc, havc tlicm as Investigations or 
of Wholes. Inquiries as they are sometimes called, as 
Arguments, or as Scientific Systems. And in con 
sidering the Methods the points to which our attention 
is to be chiefly directed, are (1) the End or Aim to be 
accomplished ; (2) the compatibility of the End with 
the Matter in which it is to be accomplished ; and 
(3) the adaptation of the Method to the Matter and the 
End. For example, we cannot produce the absolute 
certainty of demonstration in Moral Matter, or by 
means of Testimony. Nor would it be in accordance 
with the Principles of Method to prove a proposition in 
Geometry by an induction of facts, or a doctrine of 
Revelation by means of the opinions of uninspired 
men. 



IV.] METHODS OF INSTKUCTION AND CKmCISM. SECT. VH. 373 

1334. We are not to suppose that the whole of any 
book or treatise designed to convince or persuade, can 
be reduced to any Logical Formula, or will Not aii of books 
fulfil the conditions of any Method of Proof '^,f;;^li 'y^^. 
or Eefutation. Much is often thrown in for °^^^^ criticism, 
embellishment addressed to the Fancy, and much is 
designed merely to make an imj^ression upon the sen- 
sibilities and feelings either in favor of or against the 
main conclusion ; and some whole books have no other 
object than to please or amuse, or to make an impression 
upon the feelings without convincing the reason. Even 
books designed to convey instruction do not necessarily 
contain much or even any argument. They may be oc 
cupied with stating facts alone, from which no conclu- 
sion is designed to be drawn. 

1335. An impression made by a description, a nar- 
rative, a sarcasm, or a jeer, may often be a more 
eflicient motive of action than a conviction 

of the understandin£>: produced by facts and upo"n SeTensi? 

-T^ , .-x ^ ' • 1 bilities more 

reasoning. Jout these impressions, unless efiective than 
under the control of the Conscience and 
Reason, are always in danger of misleading us. They 
are not, however. Fallacies. We cannot reduce them 
to Logical Formulse. We can meet them for the most 
part by arguments addressed to the Reason, designed 
to show that the course to which the impression would 
lead us is wrong. Yet it is probable that the largest 
part of mankind are governed and guided more by 
their impressions than by their convictions. Convic- 
tions alone, however, belong to the sphere of Logic 
and of Reasoning — Impressions and Persuasion to 
Rhetoric. 

1336. It is the right and privilege of the framer of 
an argument to introduce whatever terms, and to put 
them in whatever relation to each other he ^o new mat- 
may choose. We may introduce no new Jfoduced ^^ ^Hi 
ones in completing the Formula, and if he ^'^^^^• 

has not given us material enough to complete the For- 
mula, the responsibility of the failure must be his. 



374 LOGIC. — PART n. [chap. 

His language must be regarded as mere declamation, 
unfounded assertion, vox et jprmterea nihil, 

1337. And here, I take it, is the distinction between 
argument and mere assertion. The former contains 

Distinction be- ^ ^hat is ucccssary to complete the Formula 
mellf an/'S- uudcr thc rulcs already given, so as to satisfy 
sertion. ^]^q miud Completely what are the grounds 

upon which the speaker or writer would rest his con- 
clusions. But from mere assertion no form of a com- 
plete argument can be made out without introducing 
new matter ; and this would throw the responsibility 
for the Argument upon the critic who completes it, 
rather than upon the author who should have given it 
already completed. 

1338. But besides all that is addressed merely to 
the fancy and the feelings, all that is intended as mere 

instruction to be received on authority of the 
gumentf ° and tcachcr, aud all that is mere declamation, 
mere r ces. ^^^^ ^^^ ^lg^ ^j^^ artificcs or tricks to be 

separated from what properly comes within the sphere 
of Logic. These tricks have already been defined (753), 
and discriminated from Faults or Fallacies. They have 
not been enumerated ; for no diligence could collect, 
classify, and describe all the artifices of this kind which 
carelessness may let fall or cunning devise."^ Sagacity 
and constant watchfulness alone can guard one against 
falling into them himself, or being entrapped by them 
when dealing with the unscrupulous and designing. 

1339. The first step, therefore, towards a Logical 
Analysis of any work is to discriminate the Thought 
from the Rhetoric, to select all that belongs to the pro- 
vince of reasoning and intelligence, from that which is 
mere Trick or Artifice — gaseous declamation, or mere 
didactic development of Premises. 

1340. In criticising the Terms it will be necessary 
to consider whether they are properly used or not, and 

* " Quas aut incuria fadit 
Aut humana parum cavit natura." — Hok. 



IV.] METHODS OF INSTRUCTION AND CRITICISM. SECT. VII. 375 

whether a word may not be improperly used to express 
a cognition, which is after all just the one criticism of 
which is required. And if the Term be com- '^^""^• 
plex we are to consider whether the Modals and the 
Term are not incompatible ; as for example, " trian- 
gular ellipse." Or to give some illustrations from a 
book that is before me, the author speaks of " the sub- 
stantiality of motion," " absolute relativity," " ab- 
stractly extended subsistence." It is impos- contradictio 
sible to form any conception of what is inadjectis 
meant (if any thing is really meant) by such terms. 
This Fault of Terms has been called a Contradictio in 
adjectis. 

1341. In the criticism of Arguments, it will be 
necessary to identify in the first place the Conclusion 
aimed at, since this determines the whole 

with reference to which all the parts, as whoie^s of A^r- 
Terms, Premises, &c., are to be criticised, mTed"%y''the 
and in the next place to identify the subject 
of the Conclusion as that which determines the unity 
of the Formula. By means of the Subject and Predi- 
cate of the Conclusion as Minor and Major Terms, we 
are to identify the other parts of the Formula. In 
doing this we shall, of course, find all of the principles 
and statements of the preceding work called into requi- 
sition. And I trust that it will be found that nothing 
is required which is not contained more or less expli- 
citly and fully in these pages. If any thing more is 
required, the fact will serve to show how far this Trea- 
tise is from being complete. 

1342. In the Methods of Investigation and of In- 
struction the unity of the End or Object will determine 
for us what are to be regarded as Wholes, and Wholes and 
of course by the same means what are to be {Jgatlon" ^"Ind 
regarded as subordinate Parts. The means de^rmined^'V 
to any End are always the parts of any Me- the End in view. 
thod to that End. The End of an Investigation is the 
attainment of the Predicate which we are investigat- 
ing. The End of a Construction is to put our thoughts 



376 LOGIC. PART n. [chap. IV. 

into such form and order as to be communicable to 
others. To this End, division of the Subject, order in 
arranging, definition and description, and each part of 
the division — the order, the definitions, descriptions, 
comparisons, and whatever else we may have occasion 
to use, are Parts, and should be judged as Parts, sub- 
ordinate and conducive, according to the rules and 
principles already discussed ; and whether faultless or 
faulty in themselves, they are each to be approved or 
condemned, according as they shall be found conducive 
to that End or not ; always remembering that whatever 
does not conduce to the End which is most promi- 
nently before the mind, and help on towards its attain- 
ment, is a fault, a hindrance, and an annoyance. 



APPENDIX. 



EXAMPLES FOE ANALYSIS AND^ CRITICISM. 

^ 1, Of the order in criticising Arguments, 

In analyzing and criticising the following Examples, which 
have been selected with a special view to illustrate the Prin- 
ciples and Formulae of the foregoing Treatise, we shall find 
the following order useful as expediting the process. 

In the first place, in each unity or totality of an Argument 
we must ascertain what is the point to be proved — the Con- 
clusion of the Argument as a Whole. This is necessary at 
this stage. For by this only can we identify the Minor and 
Major Terms — the Subject of the Argument, and what is 
proved of it. And it is only by this process of identifying the 
Subject and Predicate of the Argument that we can identify 
the Premises, and ascertain their character and position. 

Having identified the Minor, Middle, and Major Terms by 
means of the Subject and Predicate of the Conclusion, we can 
next identify the Premises, and arrange the Matter of the 
Argument into its appropriate Formula, and complete the 
Formula if it should require completing. 

And as soon as we have done this, we shall find an advan- 
tage in disconnecting the Matter from the Form, by substitut- 
ing in the Formula some one of the Letters of the Alphabet. 
We derive the same advantage in Logical Analysis as in 
Algebra, from using the symbolical letters for the sums and 
quantities which they represent. It facilitates the process, and 



378 LOGIC. — APPENDIX. 

errors are less likely to be made, and are more easily detected 
if they are. 

In the next place we are to consider if there is any Fault 
or Fallacy in the general form or argument. It will always 
be best to look for them in the following order : 

(1) An Ignoratio Elenchi. 

(2) Any Fault in Form or in Method. 

(3) Any Fallacy in Matter or in Diction. 

If either of these defects is found, the work, whatever other 
excellencies and attractions it may have, is worthless as an 
Argument, or effort to sustain the truth of its Conclusion. 

The next step, after having selected and arranged the parts 
of the main Argument, is to separate each of the subordinate 
parts into logical wholes or unities ; remembering always that 
the unity of the Argument or Formula consists in the unity 
of its Subject. 

Having thus divided the work up into its smallest parts 
that can be regarded as wholes at all, we are to proceed to 
reduce them to the Formulae.* 

The first thing here is to identify the Conclusion, and from 
the Conclusion the Terms, Minor and Major, which are given 
in it. We are also to notice whether it be simple, complex, 
or compound ; and what is the complicity of the judgment of 
which it is compounded, with reference to its including any 
thing illicit, by this means. 

We may here consider whether there be any Ignoratio 
Elenchi, or Fault in Method in this part of the main argu- 
ment, or not ; for if there is, we need go no farther in our 
analysis of this part, since though it should be otherwise fault- 
less, it is nothing to the purpose. 

We are next to identify the Premises by means of the 
Terms which we have found in the Conclusion ; note their 
Relation, as whether Categorical, Conditional, or Disjunctive. 
Then put the elements thus given into the Formal position, 
and complete the Formula if it be not complete. 

* Most of the Scholastic Writers on Logic whose works I havo s-een, 
speak of two kinds of Syllogisms, Formal and Material; the Material Syl- 
logisms are those which contain all the Matter of a Syllogism, hut not 
stated in any recognized Formula. A Formal Syllogism is an argument 
stated in a recognized Formula. The business of Praxis is, therefore, to 
reduce Material to Formal Syllogisms. 



EXAMPLES FOR CKITICISM. 379 

In the course of this completion, we are not only to find 
the supposed or assumed Premises in Enthymemes of the various 
forms, but also the Sequence in Conditionals, the Excluded 
Middle in Disjunctives, and the identity of kind in things 
compared.* 

Having completed the Formula, we are next to consider it 
in relation to the Faults and Fallacies in the order above 
given. 

If we find the part of the main argument which is under 
examination inconclusive for any reason, we are next to con- 
sider how important it is as a part of the main argument. 
And whether a failure or not, we are carefully to estimate its 
value and its force, if it has any, as a means of establishing the 
main Conclusion. We shall find the Conclusion either a Pre- 
mise in the main Argument, or the assertion of a fact which is 
used by way of Induction, Analogy, Example, or Circum- 
stance, &c., to prove a Conclusion which is used as such a 
Premise. 

In this way we are to analyze each subordinate part of the 
main Argument, taking as an ultimate part or unity of argu- 
ment only those which have but one subject, and which there- 
fore, a^ arguments^ can be resolved no farther. 



§ 2. Examples in Categorical Syllogisms. 

1. Every effect must have had an adequate cause — the 
creation of the world is an effect ; therefore the creation of the 
world must have had a cause. 

2. He that is always in fear cannot be happy. But those 
that are conscious of guilt are always in fear ; therefore those 
that are conscious of guilt cannot be happy. 

3. Satire is a legitimate mode of exposing the failings of 
others. But the calling others by ill-names is not satire; 
therefore it is no legitimate mode of exposing their failings. 

* As it is convenient to have a name for tins fault, of passing from one 
species to another improperly (for it is one of frequent occurrence), we may- 
call it Metahasis. This, if I understand him rightly, is what Aristotle 
means when he speaks of " passing over into another species :" MerctiSatrfs 
^is rh 6.KK0 yet/OS. 



380 LOGIC. ^APPENDIX. 

4. Tyranny is an unnecessary restraint upon human liberty. 
The English government imposes no unnecessary restraint 
upon the' liberty of its subjects ; therefore the English govern- 
ment is no tyranny. 

5. No one is free who is enslaved by his appetites. The 
sensualist is enslaved by his appetites ; therefore no sensualist 
is free. 

6. All accountable beings are free agents. Men are ac- 
countable ; therefore they are free agents. 

7. Sensualists wish to enjoy perpetual gratification without 
satiety. But this is impossible ; therefore the sensualist de- 
sires what can never be attained. 

8. That which has no reality of being cannot, as cause, 
produce or be the ground of existence to any thing. Chance 
has no reality of being; therefore nothing can be properly 
ascribed to chance by way of accounting for its origin. 

9. Liberality is a means of making others happy. But it 
is not a means of making one's self rich ; therefore making 
one's self rich does not always make others happy. 

10. Murderers never escape punishment. Yet even mur- 
derers hope to elude the laws of their country ; therefore some 
who hope to elude the laws of their country do not escape 
punishment. 

11. All amiable men merit the esteem and respect of their 
fellow men. And certainly all who aim only to do good to 
their fellow men, deserve to be esteemed and respected on that 
account. Hence all who are striving to do good to others are 
amiable men. 

12. Some effectual check to the progress of seditious pub- 
lications is absolutely essential to the safety of our country. 
The total abolition of the art of printing would prove such a 
check ; therefore the art of printing should be totally abol- 
ished. 

13. No one is rich who has not enough. No miser has 
enough ; therefore no miser is rich. 

14. The things that cannot be enumerated do not exist. 
Innate ideas cannot be be enumerated ; therefore there are 
no innate ideas. 



EXAMPLES FOR CRITICISM. 381 

15. Some poisons are vegetable. But no poisons are use- 
ful drugs ; therefore some useful drugs are not vegetable. 

16. Some recreations are necessary to the preservation of 
health and spirits. All recreations, however, are liable to be 
carried to excess and be abused ; so that some things liable to 
abuse are nevertheless necessary for man. 

17. No tale-bearer is worthy of confidence. But all tale- 
bearers are great talkers; therefore great talkers are never 
worthy of confidence. 

18. That one who has been accustomed to liberty can 
never be happy in the condition of a slave is indeed true. 
But the negroes on our Southern plantations have never been 
accustomed to liberty. Hence they are content and happy in 
their present condition. 

19. " He that is of God heareth my words ; ye therefore 
hear them not, because ye are not of God." 

20. All the most bitter persecutions have been religious 
persecutions. Among the most bitter persecutions were those 
which occurred in France during the French Revolution. 
Consequently they must have been religious persecutions. 

21. That man is independent of the caprices of Fortune 
who places his chief happiness in moral and intellectual excel- 
lence. A true philosopher is independent of the caprices of 
Fortune ; therefore a true philosopher is one who places his 
chief happiness in moral and intellectual excellence. 

22. Of two evils the less is to be preferred ; therefore 
since occasional turbulence is a less evil than a rigid despotism, 
it is to be preferred. 

23. Some objects of great beauty answer no other percep- 
tible purpose but to gratify the sight : many flowers have 
great beauty ; and many of them accordingly answer no other 
purpose but to gratify the sight. 

24. A man who deliberately devotes himself to a life of 
sensuality is deserving of strong reprobation ; but those do not 
deliberately devote themselves to a life of sensuality who are 
hurried into excess by the impulse of the passions : such there- 
fore as are hurried into excess by the impulse of the passions 
are not deserving of strong reprobation. 



382 LOGIC. ^APPENDIX. 

25. It is a difficult task to restrain all inordinate desires : 
to conform to the precepts of Scripture implies a restraint of 
all inordinate desires ; therefore it is a difficult task to conform 
to the precepts of Scripture. 

26. Any one who is candid will refrain from condemning a 
book without reading it : some Reviewers do not refrain from 
this ; therefore some Reviewers are not candid. 

27. My hand touches the pen, the pen touches the paper ; 
therefore my hand touches the paper. 

28. Lias lies above red sandstone, red sandstone lies above 
coal ; therefore lias lies above coal. 

29. A true prophecy coincides precisely with all the cir- 
cumstances of such events as could not be conjectured by 
natural reason. This is the case with the prophecies concern- 
ing the Messiah in the Old Testament ; hence these prophecies 
are true. 

30. All that glitters is not gold : tinsel glitters ; therefore 
it is not gold. 

31. No trifling business will enrich those that engage in it. 
A speculation is no trifling business ; therefore speculation will 
enrich all who are engaged in it. 

§ 3. Examples in the Hypoihetical FormulcB, 

32. If some fishes have no teeth, some animals without 
teeth are fishes. 

33. If some who are very sentimental are nevertheless not 
benevolent, then some who are not benevolent are sentimental. 

34. If fire may be separated from a flint, a property may 
be separated from its subject : but fire cannot be separated 
from the flint ; therefore a property cannot be separated from 
its subject. 

35. If hatred and malice are contrary to the Divine law, 
they ought to be avoided : that they are so no one can deny ; 
therefore they should be avoided. 

36. If the penal laws against the Papists were enforced, 
they would be oppressed and wronged. But those laws are 



EXAMPLES FOR CRITICISM. 383 

not enforced, and therefor** they have nothing to complain of 
in the way of oppression or persecution. 

37. If testimony to miracles is to be admitted, the miracles 
claimed for Mahomet are to be admitted. But as the narrative 
of those miracles cannot be admitted, no testimony to mira- 
cles is to be admitted. 

38. If the exercise of war in defence of one's country were 
sinful, it would have been forbidden in the Scripture, either 
expressly or by implication. But it is not so forbidden ; 
therefore we may safely infer that defensive wars are not 
sinful. 

39. If the fourth commandment is obligatory, we are 
indeed bound to set apart one day in seven. But no one sup- 
poses now that that commandment is obligatory. Hence there 
is no obligation to keep one day any more sacred than an- 
other, 

40. Romanism is that form of religion which has the most 
forms : and if forms are necessary to religion, then that religion 
which has the most forms is the best, and we ought all to turn 
Romanists. 

41. The adoration of images is forbidden to Christians if 
the Mosaic law was designed, not for Israelites alone, but for 
all men. It was, however, designed for Israelites alone ; hence 
the adoration of images is not forbidden to Christians. 

42. A wise lawgiver must either recognize the rewards and 
punishments of a future state, or he must be able to appeal to 
a Providence dispensing them in this life. Moses did not do 
the former, and therefore he must have done the latter. 

43. The virtues are either passions, faculties, or habits. 
But they are not passions : for passions do not depend on pre- 
vious determination. And they are not faculties : for faculties 
are possessed by nature. The virtues, therefore, are habits 
acquired by voluntary exertion and effort. 

44. The early assignment of the Epistle to the Hebrews 
to St. Paul as its author, must have been either from its being 
really his, or from its professing to be his and containing his 
name. But it makes no claim to being his. Consequently, 
nothing but a knowledge of the fact that he wrote it could 
have led the early Christians to attribute it to him. 



384 LOGIC- -APPENDIX. 

45. If the everlasting favor of Grod is not bestowed at ran- 
dom, and on no principle at all, it must be bestowed either with 
respect to men's persons, or with respect to their conduct : 
but " God is no respecter of persons ; " therefore his favor 
must be bestowed with respect to men's conduct. 

46. If every objection that can be urged would justify a 
change of established laws, no laws could reasonably be main- 
tained. But some laws can be reasonably maintained ; there- 
fore no objection that can be urged will justify a change in 
established laws. 

47. If any complete theory could be framed to explain the 
establishment of Christianity by human causes, such a theory 
would have been propounded before this time. But no such 
theory has been proposed ; therefore we may conclude that no 
such theory can be devised. 

48. If a man is ignorant he should consult others as a 
means of making up his deficiency in knowledge. If he is 
wise, yet two heads for counsel are better than one ; therefore 
in all important matters one should take counsel with others. 

49. If one is superior to others he should be polite and 
gentle in his manners towards them, as a matter of Christian 
compassion and magnanimous condescension. If he is among 
equals he should be civil and courteous, since such a demeanor 
is as much their right from him and his right from them. And 
if he is among his superiors, he should show himself courteous 
and civil, as being due to those having authority over us for 
the good of the whole, In any case, therefore, we are bound 
by the most sacred obligations to be civil and considerate of 
the feelings of others. 

50. If the Government provides for these debts by impo- 
sition, it will become odious to the people and perish. If it 
does not provide for them, it will be overthrown by the most 
dangerous of all parties, I mean extensive discontent of the 
moneyed interest. 

51. If I am under the chastening hand of God, and if there 
is no unrighteousness in Him, it must be that I am punished 
for my iniquity. 

52. If virtue is voluntary, vice is voluntary. But virtuQ 
is voluntary ; therefore so is vice. 



EXAMPLES FOR CRITICISM. 385 

53. If expiatory sacrifices were divinely appointed before 
the Mosaic law, they must have been expiatory not of ceremo- 
nial sin (for there could be none then), but of moral sin. If 
so, the Levitical sacrifices must have had no less efiicacy. In 
that case the atonements under the Mosaic law would have 
^ made the comers thereunto perfect, as pertaining to the con- 
science.' But this they could not accomplish. Hence we 
infer that expiatory sacrifices could not have been appointed 
before the Mosaic law. 

54. If transportation is not felt as a severe punishment, it 
is in itself ill-suited to the prevention of crime : if it is so felt, 
much of its severity is wasted, from its taking place at too 
great a distance to affect the feelings, or even come to the 
knowledge, of most of those whom it is designed to deter ; but 
one or the other of these must be the case : therefore trans- 
portation is not calculated to answer the purpose of preventing 
crime. 

55. Fontenelle on seeing a criminal led to punishment said, 
" There is a man who has calculated badly; " whence it follows 
that if he could have escaped punishment, his conduct would 
have been laudable. 

56. If the prophecies of the Old Testament had been writ- 
ten without knowledge of the events of the time of Christ, they 
could not correspond with them exactly ; and if they had been 
forged by Christians, they would not be preserved and acknow- 
ledged by the Jews : they are preserved and acknowledged by 
the Jews, and they correspond exactly with the events of the 
time of Christ ; therefore they were neither written without 
knowledge of those events, nor were forged by Christians. 

57. Now " if Christ be preached that He rose from the 
dead, how say some among you that there is no resurrection 
from the dead ? But if there be no resurrection of the dead 
then is Christ not risen ; and if Christ is not risen then is our 
preaching vain, and your faith is also vain. Yea, and we are 
found false witnesses against God, because we have testified of 
God that He raised up Christ whom he raised not up^ if so be 
that the dead rise not. For if the dead rise not, then is not 
Christ raised ; and if Christ be not raised your faith is vain, 
ye are yet in your sins. Then they also which are fallen 
alseep in Christ are perished." 

IT 



386 LOGIC. APPEJSTDIX. 

58. If the bishops of England, before the Reformation, 
wben tbey were nominated bj the Pope, were true and valid 
bishops, then the bishops since the Reformation, when they 
have been nominated by the Crown, are not true and valid 
bishops. But if the bishops since the Reformation, which 
have been nominated by the Crown are true and valid, then 
these before the Reformation are not so. In either case the 
claim of Apostolic succession and authority for the English 
bishops is absurd. 



^ 4. Incom;plete and Comjpouiid FormulcB. 

59. The study of Mathematics is essential to a complete 
education, because it produces a habit of close and constant 
reasoning. 

60. Familiarity is productive of contempt, inasmuch as it 
occasions a needless exposure of private failings. 

61. Man needs the restraints of law, since he is naturally 
selfish ; and is, moreover, subject to desires and passions which 
have no limits or power of restraint in themselves. 

62. Sin is hateful, because it is opposed to the Divine Will. 

63. A good face is a letter of recommendation, for it pre- 
possesses the beholder in favor of its possessor. 

64. A wise man is never surprised because he is never 
disappointed ; and he is never disappointed, because he forms 
no expectations that are not placed upon the most certain 
basis. 

65. Discord is a greater vice than intemperance, since 
discord always implicates more than one person in its guilt. 

66. Jupiter was the son of Saturn ; therefore the son of 
Jupiter was the grandson of Saturn. 

67. They who are not conscious of guilt are not subject to 
fear : hence while conscious hypocrites are always shy and 
timid, the innocent are unsuspecting and self-possessed. 

68. A negro is a man ; whoever, therefore, kills a negro 
wantonly or maliciously, is guilty of murdering a fellow man, 

69. I think : therefore I am. 



EXAMPLES FOR CRITICISM. 387 

70. Discord is not so great an evil as intemperance, for 
that generally arises from the impulse of anger ; while the lat- 
ter almost invariably proceeds from an uncontrollable appetite, 
or an inveterate habit. 

71. Americans enjoy a greater degree of political liberty 
than any other civilized people, and therefore they can have 
no excuse for sedition. 

72. Hard substances are elastic; for ivory is both hard 
and elastic. 

73. Meanness is never useful since it is always base ; and 
because it is always honorable to be honest, it is always useful. 

74. " Whosoever shall keep the whole law, and yet offend 
in one point, is guilty of the whole ; for He that said, Do 
not commit adultery, said also, Do not kill." 

75. The care of the poor ought to be the object of all laws, 
for the plain reason that the rich can take care of themselves. 

76. Wilkes was a favorite with the populace : he who is a 
favorite with the populace must understand how to manage 
them : he who understands how to manage them, must be well 
acquainted with their character : he who is well acquainted 
with their character, must hold them in contempt : therefore 
Wilkes must have held the populace in contempt. 

77. The child of Themistocles governed his mother : she 
governed her husband ; he governed Athens ; Athens, G-reece ; 
and Greece, the world : therefore the child of Themistocles 
governed the world. 

78. The Scriptures are the standard of truth : and it is 
admitted that the Church of England is in accordance with 
the Scriptures. Hoadley was in the English Church.^ But 
Hoadley denied the divine institution of Episcopacy, and the 
authority of the Church in matters of Faith. Hence no mem- 
ber of the English Church can condemn those doctrines as 
unscriptural or heretical. 

79. None but whites are civilized : the Hindoos are not 
white ; therefore the Hindoos are not civilized. 

80. None but whites are civilized : the ancient Grermans 
were whites ; therefore they were civilized. [See 332-339, 
and 587.1 



388 LOaiC. APPENDIX. 

81. None but civilized people are white ; the Gauls were 
white, therefore they were civilized. [See 587.] 

82. Popular commotions^ though commencing on a small 
scale, are so liable to ripen into systematic sedition, that they 
ought to be speedily and decisively suppressed. 

83. Every duty is accompanied with a certain propriety 
and decorum ; whatever, therefore, is not accompanied with 
propriety and decorum cannot be a duty. 

84. The Earth has been repeatedly circumnavigated ; we 
need, therefore, no other proof that it is not an interminable 
plane, as the ancients supposed. 

85. Whatever subjects fall under one and the same general 
definition are of one and the same kind ; consequently those 
things which do not fall under that definition, must differ in 
kind from each other and from all that do. 

86. Those only who understand other languages are com- 
petent to teach correctly the principles of their own ; since 
such a competency requires that philosophic view of language 
which can be acquired only by the comparison of several with 
each other. 

87. Not a man of all the antediluvians escaped except 
those that were in the Ark with Noah. Hence after the flood 
there were none who had not proceeded from him as their 
progenitor, and been acquainted with what he knew of divine 
things. 

88. Will often combats desire as it often also yields to it : 
will is not therefore desire. 

89. If Paley's system is to be received, one who has no 
knowledge of a future state has no means of distinguishing 
virtue and vice : now one who has no means of distinguishing 
virtue and vice can commit no sin : therefore, if Paley's sys- 
tem is to be received, one who has no knowledge of a future 
state can commit no sin. 

90. When the observance of the first day of the week, as a 
religious festival in commemoration of Christ's resurrection, 
was first introduced, it must have been a novelty : when it was 
a novelty, it must have attracted notice : when it attracted 



EXAJVIPLES FOR CRITICISM. 389 

notice, it would lead to inquiry respecting the truth of the 
resurrection : when it led to this inquiry, it must have exposed 
the story as an imposture, supposing it not attested by living 
witnesses : therefore when the observance of the first day of 
the week, &c. was first introduced, it must have exposed as an 
imposture the story of the resurrection, supposing it not at- 
tested by living witnesses. 

91. A system of government which extends to those ac- 
tions that are performed secretly, must be one which refers 
either to a regular Divine Providence in this life, or to the 
rewards and punishments of another world : every perfect sys- 
tem of government must extend to those actions which are 
performed secretly : no system of government therefore can be 
perfect, which does not refer either to a regular Divine Provi- 
dence in this life, or to the rewards and punishments of another 
world. 



§ 5. Miscellaneous Examples of Formulce and Fallacies, 

92. The end of a true soldier's life is the welfare of his 
country : but death is the end of a soldier's life : therefore his 
death is requisite to the safety and welfare of his country. 

93. The fish inclosed in the net were an indiscriminate 
mixture of all kinds : those that were set aside and saved as 
valuable, were fish that had been inclosed in the net : therefore 
fish of all kinds were set aside and saved as valuable. 

94. No man can possess the power to perform an impossi- 
bility. But a miracle is an impossibility ; therefore no man 
can work a miracle. [See 75.] 

95. Few scientific treatises communicate truth in a clear 
and conspicuous manner, without any admixture of error. 
Although a treatise which should so convey truth would be 
exceedingly valuable, yet it must be admitted that there are 
but fcAV treatises comparatively which are very valuable. 

96. All the miracles of Jesus would fill more books than 
the world could contain ; the things related by the Evangel- 
ists are the miracles of Jesus : therefore the things related by 
the Evangelists would fill more books than the world could 
contain. 



390 LOGIC. ^APPENDIX. 

97. If a man say, I love God, and hateth his brother, he 
is a liar ; for he that loveth not his brother, whom he hath 
seen, how can he lo^e Grod whom he hath not seen ? 

98. If the Eomish doctrine of Transubstantiation be true, 
in receiving the Eucharist, the Eomanists are guilty of can- 
nibalism. But if they are not guilty of cannibalism their 
doctrine is false. [See 221.] 

99. The principles of justice are variable ; the appoint- 
ments of nature are invariable : therefore the principles of 
justice are no appointment of nature. 

100. A story is not to be believed, the reporters of which 
give contradictory accounts of it ; the story of the life and 
exploits of Bonaparte is of this description : therefore it is not 
to be believed. 

101. It is certain that in the moral government of God, 
virtue will produce happiness and vice will produce misery. 
We may therefore say, that whatever will produce happiness 
is virtue, and define virtue to be the pursuit of happiness in 
accordance with the will of God. 

102. It is evident that drunkenness is a sin most odious 
in the sight of God. It is equally certain that the use of 
alcohol is destructive to the moral and physical energies of 
man. I claim, therefore, not only that it is the duty of every 
man to abstain totally from the use of alcoholic drinks, but 
as a good citizen and a philanthropist, to exert all his influence 
to obtain and enforce a law which shall totally prevent the 
sale of intoxicating drinks of any kind. 

103. Nothing which is of less frequent occurrence than the 
falsity of testimony can be fairly established by testimony ; 
any extraordinary and unusual fact is a thing of less frequent 
occurrence than the falsity of testimony (that being very com- 
mon) : therefore no extraordinary and unusual fact can be 
fairly established by testimony. 

104. Testimony is a kind of evidence which is very likely 
to be false ; the evidence on which most men believe that 
there are pyramids in Egypt is testimony : therefore the evi- 
dence on which most men believe that there are pyramids in 
Egypt is very likely to be false. 



EXAMPLES FOR CEITICISM. 391 

105. He who cannot possibly act otherwise than he does, 
has neither merit nor demerit in his action. A liberal and 
benevolent man in relieving the sufferings of the poor cannot 
do otherwise than relieve them : therefore there is no merit in 
his actions. 

106. Slavery is an outrage upon the inalienable rights 
of man. It operates, wherever it exists, as a means of corrup- 
tion and degeneracy to the social and political condition of 
mankind. Hence, as citizens, as Christians, and as philanthro- 
pists, we are called upon to labor for the promotion of its im- 
mediate abolition. 

107. It is generally held that St. Paul wrote the Epistle 
to the Homans. But the Epistle itself expressly declares that 
Tertius wrote it (xvi. 22). Therefore St. Paul cannot pro- 
perly be regarded as its. author. 

108. The publication of a libel is criminal : but the act 
of putting a libel into the post, is an act of publication (for the 
moment a man passes the libel from his hand his control over 
it is gone) ; that act, therefore, must be pronounced criminal. 

109. True wisdom cannot be too dearly purchased. Hu- 
mility always accompanies true wisdom : therefore humility 
cannot be too dearly purchased. 

110. No man could bind him, no not with chains ; because 
that he had been often bound with fetters and chains, and the 
chains had been broken asunder by him, and the fetters broken 
in pieces. [See 425.] 

111. That which is greater than faith and hope must be 
the highest Christian grace. Charity, therefore, which is but 
another name for almsgiving, is greater than faith and hope, 
and must therefore be more important than any degree of 
accuracy or orthodoxy in the faith. 

112. It is sufficient to show the fallacy of the Protestant 
dogma, *' the Bible, and the Bible alone is the religion of the 
Protestants," to state the fact, that many parts of the Bible 
are wanting, as for example, the Book of the Wars of the 
Lord, the Book of Jasher, and of the New Testament, the 
Epistle to the Laodiceans, to mention no more. If, thereforGk, 
the whole Bible would be a sufficient rule of faith to the 



392 LOGIC. ^APPENDIX. 

Protestant if he possessed it, yet since he has not the whole, 
what he has can be no sufficient rule. 

113. The New Testament as a distinct book, was nevei 
heard of until the Council of Laodicea, which at the earliest was 
314 years after the commencement of the Christian era. It is, 
threfore, absurd to pretend that it was written by the Apos- 
tles, who were all dead more than a century before this date. 

114. A collection of rules, designed to enable us to under- 
stand the principles of any subject, is a science ; but if those 
rules are designed to assist us in the application of these prin- 
ciples to a specific end, they constitute an art. Now Logic 
collects and states the rules with a view to the comprehension 
of the rules themselves ; but Ehetoric with a view to their ap- 
plication to the specific end of conviction and persuasion : 
therefore Logic is a science, and Rhetoric is an art. 

115. Russia knows full well that she is engaged in a eon- 
test with two nations that were never yet overcome by valor 
of arms, nor circumvented by fraud or cunning in diplomacy. 
But Russia is contending against France and England : there- 
fore neither France nor England was ever overcome by valor, 
or circumvented by cunning or fraud. 

116. If the forgiveness of sins was imparted at one's con- 
version, Ananias could not have said to St. Paul three days 
after his conversion, '' Arise, be baptised, and wash away thy 
sins.'' But such was precisely the message which he was 
commissioned by the Holy Ghost to deliver to him ; therefore 
remission of sins takes place in Baptism. 

117. An unholy minister is the greatest of all sinners ; 
for either he is a person of more than ordinary knowledge or 
he is not. If he is not, he sinned greatly in undertaking that 
office, for which so great knowledge is required. If he be, his 
knowledge will doubtless increase his guilt. 

118. The works of creation imply far more of design and 
of wisdom than the Iliad of Homer or the Geometry of Euclid. 
But no one ever supposed that the Iliad, or the Geometry of 
Euclid were composed without an intelligent author; there- 
fore the works of creation must have had an Intelligent 
Creator. 

119. The Jesuit cites Ruffinus in proof of the infallibility 



EXAMPLES FOR CRITICISM. 393 

of his church. But if Ruffinus is right the church is not in- 
fallible, since it does not agree with Ruffinus. If, however, 
Euffinus is wrong, his testimony is worthless. 

120. The doctrine which holds to an omnipresent divine 
power and agency in the operations of Nature, is as contrary 
to the Scriptures as it is to sound philosophy ; for the Scrip- 

.tures say expressly, " the earth bringeth forth fruit of herself ^^ 
(St. Mark iv. 28). 

121. Nature is either the author of Nature, or it is the 
order of things established by a Supreme Intelligence. But 
nothing can be the author of itself; therefore. Nature can be 
only the order of things established by a Supreme Intelli- 
gence. 

122. The cause of evil is itself an evil. But that Chris- 
tianity has caused much evil in the shape of wars, oppression, 
imposture, fanaticism, and persecution, cannot be denied. 

123. Our Lord said, " If a man keep my saying he shall 
never taste of death. Then said the Jews unto Him, Now we 
know that thou hast a devil. Abraham is dead, and the Pro- 
phets. Art thou greater than our father Abraham ? whom 
makest thou thyself ? " 

124. " The argument of the atheist assumes that it is pos- 
sible to create an intelligent moral agent, and place it beyond 
all liability to sin. But this is a mistake. Almighty Power 
itself cannot create such a being, and place it beyond the pos- 
sibility of sinning, as we shall prove," &c. 

125. He who has a confirmed habit of any kind of action, 
exercises no self-denial in the practice of that action ; a good 
man has a confirmed habit of virtue ; therefore he who exer- 
cises self-denial in the practice of virtue is not a good man. 

126. He is the greatest lover of any one who seeks that 
person's greatest good ; a virtuous man seeks the greatest 
good for himself; therefore a virtuous man is the greatest 
lover of himself. 

127. Whatever is real is limited [by that which it is not]. 
But whatever is limited is not infinite ; therefore if God is 
real, and not a mere fiction of the imagination. He is not an 
infinite being. 

17^ 



394 LOGIC. APPENDIX. 

128. Theft is a crime : theft was encouraged by the laws 
of Sparta ; therefore the laws of Sparta encouraged crime. 

129. Every hen comes from an egg : every egg comes from 
a hen : therefore every egg comes from an egg. 

130. Nothing is heavier than platina : feathers are heavier 
than nothing : therefore feathers are heavier than platina. 

131. Meat and drink are necessaries of life : the revenues 
of Vitellius were spent on meat and drink; therefore the 
revenues of Vitellius were spent on the necessaries of life. 

132. No evil should be allowed that good may come of it. 
But all punishment is an evil ; therefore no punishment should 
be allowed. 

133. Repentance is a good thing. But no persons have 
so much repentance as the wicked ; therefore none have so 
much good as the wicked. 

134. He who bears arms at the command of the magis- 
trate does what is lawful for a Christian. The Swiss in the 
French service, and the British in the American service bore 
arms at the command of the magistrate ; therefore they were 
doing only what was lawful for a Christian to do. 

135. He who calls you a man speaks the truth ; but he 
that calls you a knave calls you a man ; therefore he who calls 
you a knave speaks the truth. 

[This Minor Premise may be prononnce-d a non vera. But I should 
prefer to refer the Formula to the Fallacy of Accidents (750, 1057-8). 
In this view we must regard as accidental, that which is not in the Con- 
ception when used as a Predicate (195), however essential it may be to 
the existence of any individual in that genus among the reahties of 
being.] 

136. A monopoly of the sugar-refining business is bene- 
ficial to sugar-refiners ; and of the corn- trade to corn-growers ; 
and of the silk-manufacture to silk-weavers, &c., &g. ; and 
thus each class of men are benefited by some restrictions. 
Now all these classes of men make up the whole community ; 
therefore a system of restrictions is beneficial to the community. 
[See 58-60, 748.] 

137. " We have seen in a preceding chapter, that naturally 
no man has any authority over another — his pursuits, his posses- 
sions, his life or his liberty, except what arises from the pri- 



EXAMPLES FOR CRITICISM. 395 

mary law of nature, self-defence. Now as a State is made np 
of men, the State can have no authority which each man in the 
State did not possess before he entered into the body politic. 
And from this it follows, not only that capital punishment, 
banishment, and such like punishments are unauthorized and 
wrong, but that all attempts on the part of the State to pro- 
mote education, impose oaths, or to encourage religion in any 
form, or to regulate the institution of marriage in any way, 
is a tyrannical assumption of rights over man, which power 
may indeed enable it to enforce," &c., but nothing can jus- 
tify. [58.] 

138. If the difference in the various races of men has not 
been produced by climatic causes, they must each of them have 
had a separate proto-plastic pair for their progenitors. But 
these differences cannot have been produced by climatic causes ; 
therefore the races cannot have sprung from the same parents 
originally. [See 400 and 412.] 

139. Opium is a poison ; but physicians advise some of 
their patients to take Opium ; therefore physicians advise 
some of their patients to take poison. 

140. Animal food may be entirely dispensed with (as is 
shown by the practice of the Brahmins and of some monks) : 
and vegetable food may be entirely dispensed with (as is plain 
from the example of the Esquimaux and others) : but all food 
consists of animal food and vegetable food ; therefore all food 
may be dispensed with. 

141. I have shown, gentlemen, that it is the natural right 
of all God's creatures to be free. I have shown that a 
people having the same tongue, historic recollections and 
associations, conveniently situated, and existing in sufficient 
numbers for the purpose, are entitled to a distinct national 
existence ; and I claim, therefore, not only the sympathy of 
Americans for my poor and oppressed Hungary, which I know 
that I shall have, but also their intervention as a nation, and 
their generous liberality in furnishing the material aid neces- 
sary to enable us to carry on our struggle, and secure our 
independence of Austrian rule and despotism. 

142. Whilst all other sorts and orders of men conversed 
with our Lord, never do we hear of any interview between 
Him and the Essenes- Suppose one Evangelist to have 



396 LOGIC. APPENDIX. 

overlooked such a scene, another would not. One Evangelist 
was impressed with one scene and a second bj another. And 
thus it must have happened that, amongst the four, at least 
one would have noticed the Essenes. But no one of the four 
Gospels alludes to them. The Acts of the Apostles is a fifth 
body of recollections, but this does not notice them. The Apo- 
calypse of St. John says not one word about them. St. Peter 
and St. James in their Epistles entirely overlook them. St. 
Paul gives no sign that he had ever heard of them. Where- 
fore we must conclude that there was no sect known by that 
name, except in the delusions conjured up by his own igno- 
rant heart (Josephus). 



^ 6. Examples presenting Questions of Method, 

143. All the facts of man's mental activity may be referred 
to two classes. Spontaneity and Eeflection. But of the two 
classes, the spontaneous must be first in point of time. For 
reflection implies volition, and volition implies that the thing 
chosen is already in the mind, as an object of conscious 
thought before the choice. Hence it could not have been given 
in reflection, and must therefore have been given in spon- 
taneity. 

144. " With God nothing is impossible.' ' But God can- 
not make the three angles of a triangle more than two right 
angles ; therefore some things are impossible with God. [See 
428, 424.] 

145. The religion of the ancient Greeks and Romans was 
a tissue of extravagant fables and groundless superstitions, 
credited by the vulgar and the weak, and maintained by the 
more enlightened, from selfish or political views : the same 
was clearly the case with the religion of the Egyptians : the 
same may be said of the Brahminical worship of India, and 
the religion of Fo professed by the Chinese : the same of the 
romantic mythological system of the Peruvians, of the stern 
and bloody rites of the Mexicans, and those of the Britons and 
of the Saxons : hence we may conclude that all systems of 
religion, however varied in circumstances, agree in being super- 
stitions kept up among the vulgar, from interested or political 
views in the more. enlightened classes. 



EXAMPLES FOK CRITICISM. 397 

146. A feeble Executive implies a feeble execution of the 
Government. A feeble execution is but another name for a 
bad execution ; and a government ill executed, whatever it 
may be in theory must be in practice a bad government. 
Hence with a feeble or inefficient executive, a government 
will always be bad, whatever may be its form or its theory. 

147. In the Scriptures it is written concerning the Church, 
and we see that the Church exists. There it is written con- 
cerning idols that they shall cease, and we see that they are 
not. There it is written that the Jews were to lose the king- 
dom, and we see that the fact is so. There it is written con- 
cerning heretics that they should exist, and we see that it is so. 
There it is written also concerning the Day of Judgment. There 
it is written concerning the rewards of the good and the punish- 
ment of the wicked. In all things we have found Grod faith- 
ful. Will He fail and deceive us in the last ? 

148. I maintain that the Fugitive Slave Law is uncon- 
stitutional, or at least a law not required by the Constitution. 
'^ Slaves''^ are not mentioned in the clause requiring the ren- 
dition of persons held to service in one State escaping into 
another. The gentlemen [of the South] say indeed that slaves 
are Id eluded in the scope and intent of the law. But I answer 
so are undoubtedly the Negroes, who have been admitted to 
citizenship in the Northern States, included in that clause of 
the Constitution which declares that the '^ citizens of each 
State are entitled to the privileges and immunities of citizens 
in any of the other States into which they may go to reside." 
And they exclude Negro citizens of the Northern States from 
citizenship in their States, if they choose to go into their 
borders. 

149. St. Paul says, " Whom God did foreknow He also did 
predestinate to be conformed to the image of his Son. More- 
over whom He did predestinate them He also called, and whom 
He called them He also justified, and whom he justified He 
also glorified." But Christians, so long as they are living in 
the body are not glorified ; therefore they are not among those 
of whom St. Paul was speaking as predestinated by God to be 
conformed to the image of His Son. 

150. If these acts are valid, the old corporation is abol- 
ished and a new one created. The first act does, in fact, if it 



398 LOGIC. ^APPENDLX. 

can have any effect, create a new corporation^ and transfer to it 
all the property and franchises of the old. The two corpora- 
tions are not the same in any thing which essentially belongs 
to the existence of a corporation. They have different names 
and different powers, rights and duties. Their organization is 
wholly different. The powers of the corporation are not vested 
in the same or similar hands ; and the act itself provides for 
the first meeting and organization of the new corporation. It 
expressly provides that the new corporation shall have and 
hold all the property of the old ; a provision which would be 
quite unnecessary upon any other ground than that the old 
corporation was dissolved. 

151. It has been noticed that when we see a good act per- 
formed, we approve the act and feel a sympathy with the agent. 
It has hence been laid down as a fundamental principle in 
Ethics, that those actions are good which thus elicit our sym- 
pathy and approbation. But this is a false criterion. It implies 
a judgment concerning the act, " it is good," and a feeling or 
emotion, and holds that the judgment is based upon the emo- 
tion. But the judgment precedes and is the cause of the 
emotion, for the emotion will always remain the same so long 
as our estimate of the act remains unchanged. But let us 
hear something concerning the act which changes our estimate 
of its character, and the emotion or feeling towards the person 
who performed it changes also. 

152. If a paste be made of wheat flour, boiled in water, 
and allowed to stand for a few days, there will be in it not 
only small plants or vegetables, but also small animalculse. 
Now the boiling would of itself have destroyed all the seeds 
of vegetables, as well as the ova of any animal existence, so 
that we are led inevitably to the conclusion that inorganic 
matter will produce both vegetable and animal life, without 
the seeds or ova of preceding plants or animals of the same 
species ; and if so, the theory of creation, and a personal 
Creator, is shown to be unnecessary to philosophy, and even 
unphilosophical. 

153. It is said that at death all appearance of life becomes 
extinct, and every indication of a total cessation of existence 
is presented. 

But in the first place we see that parts of the body, as 



EXAMPLES FOR CRITICISM. 399 

hands, feet, &c., may die and decay, and the soul remain en- 
tirely unimpaired. 

Again, it is a principle which prevails every where in 
Nature, that nothing once in existence can be lost. The wood 
that is consumed in the fire is resolved thereby into its ele- 
ments, but every particle of it exists somewhere. So with the 
body at death. But the soul being immaterial is not capable 
of dissolution, or resolution into constituent elements. 

Again, we have frequent cases of change of the form of 
existence, without a cessation of the existence of that whose 
form is changed. Such changes we have in the foetus in 
passing from its state before birth to its mode of life after ; in 
the chick emerging from the shell, and especially in the case 
of all the metabolians which appear as worms : these go into a 
state of apparent death, and after a while emerge as insects 
with wings. 

In all these cases that which is once in being, continues 
to exist notwithstanding the changes in its form or state of 
existence. Hence we may conclude that the human soul will 
do so likewise at death. 

154. Some years since there appeared in the West a dis- 
ease, which was called the milk-sickness. The following hypo- 
theses were suggested as accounting for it ; namely, that (1) it 
proceeded from some miasma in the air ; (2) from some pecu- 
liarity in the water ; (3) from arsenic, cobalt, and other mine- 
rals in the soil ^ and finally, (4) that it was owing to sorae 
disease in the vegetable productions. 

As facts it was found : (1) that its appearance was con- 
fined within narrow limits ; (2) that when it makes its appear- 
ance among men, there has been preceding it a disease among 
the animals, called the Sloivs or Trembles. It is also ascer- 
tained (3) that the flesh, the milk, the butter, and the cheese 
made from animals having the Slows, causes the milk-sickness 
in men [hence its name] ; (4) the disease appears in pastures 
where there is no water ; and (5) the flesh of animals diseased 
imparts none of its poisonous properties to the water in which 
it is boiled ; (6) the disease affects those animals which graze 
at night, and especially in the woods ; (7) carnivorous animals 
never have the disease until they have taken it by eating ani- 
mals already affected ; and (8) females during lactation, cows, 
sluts, &c., often escape the disease themselves after having 



400 LOGIC. ^APPENDIX. 

eaten the poison, but communicate it to their oflPspring. And 
(9) in those cases in which the flesh of diseased animals had 
been swallowed and vomited up soon afterwards, there was 
either no disease or only very little following. [To be treated 
as a case of Elimination.] 

155. The various systems of pagan idolatry correspond so 
closely, that they cannot have been struck out independently 
in the several countries where they have been established, and 
must therefore have originated from a common source. But 
if they had a common source, then either one nation must have 
communicated its peculiar theology to every other people in 
the way of peaceful and voluntary imitation, or through the 
medium of conquest and violence ; or all nations must have 
been assembled together in a single community, and then agreed 
to adopt the theology in question as a new and recent inven- 
tion ; or, having received it from the past, and believing it on 
whatever grounds to be true, they must have carried it with 
them as from that common centre to all parts of the globe. 
The first and second are impossible in the nature of things ; 
therefore all these various systems must have had a common 
origin. 

But the third position is nearly as incredible as either the 
first or the second ; namely, that they should have all agreed 
in one stupendous system of imposture, professing to believe 
as divine that which they knew that they had of themselves 
but recently invented. 

Idolatry, therefore, must have arisen before the dispersion 
of mankind, and be a corruption of a tradition that was be- 
lieved true at an age so near to the origin of the race (or its 
restoration after the flood), that its foundation must have been 
in the truths which were either observed by man, or super- 
naturally communicated to him at the time of his creation. 

156. The fundamental doctrines and institutions of Chris- 
tianity are not to be held as mere opinions, with regard to 
which men may innocently diff'er, and be entitled in their diver- 
sities to that consideration and respect to which they are enti- 
tled in matters of mere indifi'erence or uncertainty. For other- 
wise no persons could be allowed to afiirm the truth with that 
confidence and certainty which its proper influence requires. 
It follows, moreover, from the wisdom and justice of God, that 
the evidence of the truth of those doctrines and institutions is 



EXAMPLES FOR CRITICISM. 401 

such that they cannot be innocently rejected. If God is infi- 
nitely wise he knew what was sufficient evidence, and if He is 
just He would never require belief and obedience without giv- 
ing such evidence as would throw the guilt of unbelief upon 
the unbeliever. And in all other cases, in all departments of 
thought, we hold to certain fundamental principles with regard 
to which we allow of no difierences of opinion, which we ac- 
knowledge to be entitled to respect. In Geometry, in Astro- 
nomy, in Mechanics, every where in fact, we expect the assent 
of all intelligent and well-disposed men to certain fundamental 
principles. We do not treat the man who pretends to science, 
and yet denies that the earth revolves on its axis around the 
sun, instead of the sun's moving around the earth as entitled 
to argument. We regard him as either a fool or a madman. 
In like manner the Articles of Faith contained in the Apos- 
tles' Creed, the Ministry, the Worship, and the Sacraments of 
the Church, have been held in all ages of the Church as too 
fundamental in their character, and too fully and obviously 
revealed in the Scriptures, to be properly regarded as mere 
subjects of opinion and preference, in regard to which unbelief 
could be innocent or properlv entitled to favor. 



^ 7. Abstract of Leslie's Short and Easy Method. 

'' What you ask and I undertake to accomplish, is to furnish 
some one topic of reason which shall demonstrate the truth of 
the Christian Religion, and at the same time distinguish it 
from the impostures of Mahomet and whole pagan world." 

'^ If the matters of fact which are recorded in the Gospels 
be true, the truth of doctrine of Christ will be sufficiently 
evinced ; for if His miracles be true they do vouch the truth 
of what He delivered." 

'' The same is to be said as to Moses and the Old Testa- 
ment." 

I shall then first lay down such rules as to the truth of 
matters of fact in general, that where they all meet, such mat- 
ters of fact cannot be false. And then, secondly^ I shall show 
that all these rules do meet in the matters of fact of Moses and 
of Christ ; and that they do not meet in the matters of fact of 
Mahomet and the Heathen deities, nor can possibly meet in any 
imposture whatever. 



402 LOGIC. ^APPENDIX. 

I. The Kules are : 

1st. That the matters of fact be such as that men's out- 
ward senses, their eyes and ears may be judges of it. 

2d. That it be done publicly in the face of the world. 

3d. That not only public monuments be kept up in memory 
of it, but some outward actions to be performed. 

4th. That such monuments, and such actions or observ- 
ances be instituted, and do commence from the time that the 
matter of fact was done. 

The two first rules make it impossible for any such matter 
of fact to be imposed upon men at the time when such matter 
of fact was said to be done. 

The only alternative, therefore, is that such matter of fact 
might be invented some time after. 

But against this the two last rules (3d and 4th) secure us, 
as much as the two first rules in the former case. 

II. The matters of fact of Moses and of Christ have all 
these rules or marks before mentioned, and that neither the 
matters of fact of Mahomet, nor what is reported of the Hea- 
then deities have the like, and that no imposture can have 
them all. 

As to Moses. He persuaded the Israelites that he had 
brought 600,000 of them from Egypt and through the Red 
Sea, that he fed them forty years without bread by a miracu- 
lous manna. But he could not have persuaded them of these 
facts if they had not been true, since every man's senses that 
were then alive must have contradicted it. So that here are 
the first and second of the above-mentioned four marks. 

For the same reason it would have be.en impossible for 
him to persuade them to receive his five Books (the Penta- 
teuch) as truth, unless they were so ; since in those books he 
constantly appeals to them as eye and ear witnesses of those 
things. 

The utmost that we can suppose then is, that these Books 
were written in some age after Moses and put out in his name. 

But in that case it is impossible that the Books should 
have been received, for they speak of themselves as delivered 
by Moses, and kept in the Ark from his time, and likewise a 
copy with the King. 

Now in whatever age we may suppose the imposture to 
have been attempted, it was impossible that it should be 



EXAMPLES FOK CRITICISM. 403 

received as truth, since no such copy would have been in ex- 
istence in the Ark or in the King's possession, as the Book 
itself claims. 

But besides this the Book speaks of laws and ordinances, 
and of the time and circumstances of their origin, and claims 
that they had been observed from the time of their origin, as 
of the Passover, the institution of the Levites, the budding of 
Aaron's rod, which was still kept in the Ark, the pot of manna, 
the brazen serpent, and the Feast of Pentecost. Then there 
was also the Sabbath, the daily sacrifices, the yearly expiation, 
the new moons, and other monthly, weekly, and daily remem- 
brances and recognitions of these things. Here then the third 
Sind fourth marks mentioned above are found. 

But suppose that these things had been practised before 
the Books of Moses were forged ; that these Books imposed 
upon the people only in making them believe that they had 
kept these observances in memory of what had never occurred. 

Now this supposes that the Jews kept these observances 
either in memory of nothing, or without knowing what they 
commemorated. 

But the observances themselves express the ground and 
reason of their being kept. 

Again, suppose the Jews did not know any reason why 
they kept these observances, and that they were persuaded 
that they had been keeping them as observances of that of 
which they had never heard before. 

Does any Deist think it possible that such a cheat could pass ? 

Secondly, all these four marks do meet in the matters of 
fact which are recorded in the Gospel, of our Saviour. For the 
two first : the miracle of feeding three thousand at one time ; 
five thousand were converted at one time by what they had 
seen — miracles that were done publicly and before their own 
eyes. Then for the two last : Baptism, the Lord's Supper, 
were instituted as memorials of what was then done ; and the 
institution of the Ministry, which has continued by a regular 
succession to this day, in all which respects the matters of fact 
of the Gospel narrative as completely fulfil the four rules as 
those that are related of Moses. 

III. The matters of fact of Mahomet and the fabled dei- 
ties, do all want these four marks. 

First, Mahomet did not claim in his day to have performed 
any miracles. 



404: LOGIC. APPENDIX. 

Secondly, those that are told of him want the first two 
rules ; they were not performed in the presence of any one, 
and we have only his word for them. 

The same is to be said of the fables of the Heathen gods. 

It is true that the Heathen deities had their priests. They 
had also feasts and games, and other institutions in memory 
of them. But all these want the fourth mark, they were not 
instituted at the time of the occurrence of the events which 
they claim to commemorate ; and their priests were not ap- 
pointed by the gods, but only by others in honor of them. 
And therefore these orders of priests are no evidence to the 
truth of the matters of fact which are reported of their 
gods. 

IV. Now to apply what has been said. You may challenge 
all the Deists in the world to show any action that is fabulous, 
which has all the four rules or marks before mentioned. No, 
it is impossible. And (to resume a little what has been spoken 
of before) the histories of Exodus, and the Gospel, never could 
have been received, if they had not been true ; because the 
institution of the Priesthood of Levi, and of Christ ; of the 
Sabbath, of the Passover, and of Circumcision ; of Baptism, 
and of the Lord's Supper, &c., are there related as descend- 
ing all the way down from those times, without interruption. 
And it is full as impossible to persuade men that they had 
been circumcised or baptized — had circumcised or baptized 
their children — had celebrated passovers, sabbaths, sacra- 
ments, &c., under the government and administration of a cer- 
tain order of priests, if they had done none of these things, as 
to make them believe that they had gone through seas upon 
dry land, seen the dead raised, &c. And without believing 
these, it was impossible that either the Law or the Gospel 
could have been received. 



^ 8. Mr. Webster's Argument in the Girard Will Case. 

This Will devises a certain sum of money to be appro- 
priated to the erection and support of a College (10).* 

The first question is whether this devise can be sustained 

* These numbers in parentheses refer to the page in the printed speech, 
from which the statements preceding them are taken. 



EXAMPLES FOR CRITICISM. 405 

otherwise than as a charity. If the devise be a good limita- 
tion at law, if it require no exercise of the favor which is 
bestowed upon privileged testaments, there is already an end 
to the question — this point is conceded. 

The devise is void according to the general rules of law, 
on account of its not mentioning the persons to whom the be- 
quest is made. 

The bequest must stand then, if it stand at all, on the pecu- 
liar rules which equitable jurisprudence applies to charities. 

But I maintain that neither by judicial decisions, nor by 
correct reasoning on general principles, can this devise or be- 
quest be regarded as a charity ; (11) because. 

It is derogatory to the Christian Religion. 

It tends to weaken men's reverence for that Religion, and 
their conviction of its authority and importance ; and, there- 
fore, it tends in its general character to mischievous and not 
to useful ends. 

The College is founded to promote infidelity, and a gift or 
devise for such objects is not a charity (12). 

The object of this bequest is against the public policy of 
the State ; therefore the devise ought not to be allowed to 
take effect. 

These are the two propositions which it is my purpose to 
maintain on this part of the case (12). 

The Will excludes all Ministers of the Gospel from the 
College (13). 

There is no Christian charity that excludes the Minis- 
try (16). 

It has so been understood from the time of Constantino 
down to our own (16). 

The opening counsel admitted that there is no charity 
without Christianity (19), and I maintain that wherever 
the authority of God is disowned, the duties of Chris- 
tianity derided, and its Ministers shut out, there can be 
no charity (19, 20). 

He who rejects the ordinary means of accomplishing an 
end means to defeat that end itself, or else he has no meaning ; 
this is true even if the means be but of human appointment, 
although the end rested on divine authority. But if the 
means be of divine authority also, then the rejection of them 
is direct rejection of that authority (30). 



406 LOGIC. APPEKDIX. 

But nothing is more certain in Christianity, than that the 
Author of the Christian Religion Himself did appoint a Chris- 
tian Ministry. 

He who does not believe this cannot believe the rest (31). 

This Ministry have continued to our day, and gone over 
the whole world performing their work. Nowhere has any 
part of the globe been Christianized without the Ministry. It 
is therefore idle mockery to pretend that that man has any 
respect for the Christian Religion who derides and rejects its 
Ministers (32). 

In the next place this scheme of education is derogatory to 
Christianity, because it proceeds upon the presumption that 
Christianity is not the only true foundation, or any necessary 
foundation of morals. 

So the world has not thought. 

The Word of God declares otherwise in the Decalogue (34). 

Christ taught otherwise (35). 

Reason and human nature teach otherwise (35, 36). 

Again, the Will excludes the observance of the Christian 
Sabbath. 

But the Christian Sabbath is a part of Christianity. This 
is admitted by all Christians (37), and the Will excludes the 
means for observing the Sabbath (37, 38). 

And where the Christian Sabbath is not observed, there is 
no public worship of God. 

But the reasons assigned for the exclusion of Christianity 
from the College, are still more derogatory to Christianity. 

They are that the evils resulting from the diversity of 
opinions and sects, is greater than the good which Christianity 
itself produces ; whence he infers that we should cut up Chris- 
tianity by the roots (42). 

But this mode of reasoning, if it were allowed, would 
destroy men's social relations and all human institutions (46, 
47). 

But there is a settled policy of the State of Pennsylvania ; 
this is not denied ; and Christianity is a part of that policy. 

Any school or system of education which is contrary to 
that policy, cannot be sustained by the State (65). 

The Courts of Pennsylvania have declared that a charitable 



EXAMPLES FOR CRITICISM. 407 

bequest which counteracts the public policy of the State can- 
not be sustained (67). [The case of Methodist Church vs. 
Remington and the 8th of Johnson, p. 291.] 



^ 9. Mr, Dana's Argument in the Ellsworth School Case, 

This was a suit brought by Laurence and Bridget Donahoe 
against Richards and others, Superintending Committee of 
Schools, claiming damages of the Committee for having ex- 
cluded the Plaintiffs from the benefit of the common schools, 
by making the reading of the Bible, in the common English 
Version, obligatory upon all the pupils. The Plaintiffs being 
Roman Catholics could not comply, on grounds of conscien- 
tious scruples. 

This is a novel suit ; there is no one like it in the Reports. 

The general principle of law is, " that a public officer exer- 
cising a discretion, judicial in its character, cast upon him by 
the law, is not liable to private actions for damages, unless he 
acts in bad faith or from malice." 

But in this case it is not pretended that there was malice 
or bad faith (6). 

By the constitution and laws of Maine it is the duty of the 
Committee, " to direct the general course of instruction, and 
what books shall be used in the respective schools." In the 
exercise of this authority, the Committee continued the use of 
the Bible in the common English Version (7). 

By authority of the State also they have power to expel 
from any school, any pupils who shall not comply with the 
regulations which they have made (7). 

Now the point whether the Defendants in this suit are lia- 
ble has never been decided. 

But in the case of Wheeler vs. Patterson, 1 K H. 88, it 
was decided that Selectmen of a town, were not liable for 
refusing a man his privilege of voting, even though they were 
wroDg in their act, " so long as their motives are pure and 
untainted with fraud and malice." 

In the case of Griffin vs. Rising, 11 Met. 339, it was held 
that Assessors were not liable for refusing to tax a man, al- 
though he lost his vote thereby, on the ground that they " are 



408 LOGIC. APPENDIX. 

exempted from liability for damages when acting with in- 
tegrity." 

In Allen vs. Blunt, 3 Story 141, it was held that, " where 
a particular duty is confided to a public ofiicer, to be exercised 
by him at his discretion, upon an examination of facts, of 
which he is made the appropriate judge, his decision is con- 
clusive." 

In 7 Howard 89, and 12 Howard 390, it was held that the 
commander of a ship was not responsible for the punishment 
of a marine, though he were innocent, so long as he did it not 
from malice, and that he was not responsible for error of law, 
or in his judgment of facts if he acted in good faith. 

All these cases are analogous to the one before the Court. 
The only exception is the case of Lincoln vs, Hapgood. This 
decision, however, has been overruled. 

But not only are the defendants not liable for damages in 
this suit. The continuance of the use of the Bible is a rea- 
sonable exercise of their discretionary power. 

It has always been used in the schools of Maine, 

The Defendants are obliged by law to see that the princi- 
ples of morality and all the virtues shall be taught in the 
schools. But how can principles of morality be taught except 
on the basis of religion ? A system of morality not founded 
on religion is not morality, but only a system of self-interest. 

The objection however is not, they say, to the Bible, but 
to our English Version of it. 

But " great portions of the translation were made by men 
in the bosom of the General Church before the Reformation." 
Testimony to its accuracy has been borne by learned men of 
the Roman Church. 

As a fountain of pure idiomatic English it has no equal in 
the world. From it we derive our household words. Hence 
as a preparation for life, an acquaintance with the common 
English Bible is indispensable, while the Romish Version is 
un-English. 

But the effect of this objection is to exclude the Bible 
altogether. Each denomination has a translation, or at least 
prejudices and peculiar views of its own. If one is to insist 
on his version, others will ; and all will be excluded. The 
question, therefore, is whether the Bible shall be read at all 
or not. 



EXAIVIPLES FOR CRITICISM. 409 

It only remains to consider the constitutional objections 
against the law under which the Committee acted. 

The power to regulate schools and determine what studies 
shall be pursued, and what books read, must be lodged some- 
where. The Constitution of Maine gives the Legislature 
power " to make and establish all reasonable laws and regula- 
tions for the defence and benefit of the people, not repugnant 
to the Constitution of Maine, or to that of the United States." 
And if this power to select books, and suspend or refuse chil- 
dren for disobedience, were not expressly given in the Consti- 
tution, it would be implied in the necessity of the case (Sher- 
man vs. Charlestown, 8 Cush. 161 ; and Spear vs. Cummings, 
22 Pick. 223). 

It is said that the schools are public, and that all resident 
tax-payers have a vested right in them. 

But this right must be enjoyed subject to restrictions and 
limitations, necessary for the good and rights of others. This 
does not subject one denomination to another, but the choice 
of a few to the good of the many. 

The only constitutional question worthy of attention, is 
that which arises from the clause which declares that " no one 
shall be hurt, molested, or restrained in his person, liberty, or 
estate for his religious opinions." 

This clause was intended to guard against persecution, 
directed against person or property. But there is no such 
persecution in this case ; whatever inconvenience may have been 
suffered, is the incidental and indirect consequence of the 
opinions which the Plaintiffs choose to hold. 

But if they were ^' hurt or molested," in the sense of the 
Constitution, still the act of the Committee is not unconstitu- 
tional. 

It is a constitutional provision, for instance, that no man's 
property shall be taken for public uses without compensation. 
And yet the Legislature has full power to regulate the manner 
in which men shall use and enjoy their property, so as to pre- 
serve the rights of the public. In this exercise of legislative 
power, a man's property may sometimes be much diminished, 
or even destroyed, and he have no remedy. 

In the Warren Bridge case it was established that the 
State may impair or destroy the value of an existing franchise 
for the public good, and that no compensation need be made, 

18 



410 LOGIC. ^APPENDIX. 

if it be not confiscated or abolished. The daily making of 
highways, railroads, and canals for the public good, is con- 
stantly impairing the value of some private property, and in 
some cases totally destroying it, and yet no compensation is 
made. 

In the case of Tewksbury it was held (11 Met. 55) that the 
State might prohibit Mr. T. from taking sand from his own 
beach. So in Alger's case (7 Cush. 53), burials in cities may 
be prohibited without compensating the owners of vaults for 
their loss, however costly or valuable they may have become. 
The Sunday laws also are held to be constitutional, although 
the Jews, by reason of their religious profession, lose one sixth 
of their working life, and are '' hurt and restrained in their 
liberty and estate," and put to an inequality with Christians. 

The Constitution prohibits religious tests as qualifications 
to office. Yet all judicial officers are required to administer 
oaths, although the Quakers regard the taking of oaths as un- 
lawful. 

Hence we must conclude that the power of the Committee 
is not rendered unconstitutional, by the mere fact that it inci- 
dentally operates to the disadvantage of an individual who, by 
his opinions or preferences, has put himself in opposition to 
the laws of the land and the acts of its legitimate authorities. 



INDEX 

OF SUBJECTS AND OF THE TECHNICAL TERMS OCCURRING 

IN THE WORK. 



Abscissio Infiniti 24:1, its uses 241, 
242. 

Absolute truth, proved only by 
Demonstration 325. 

Abstract, knowledge of the, subse- 
quent to that of the concrete 361. 

Abstract Terms explained 14. 

Abstraction what 215. 

AcATEGOREMATic Tcrms 13. 

Accidents separable and insepara- 
ble 19, predicated of aU subjects 
56, FaUacy of 191. 

Accidental. Properties may be- 
come Formal 222, may become 
Material 284, may become Essen- 
tial 310. 

Achilles and the Tortoise, sophisms 
of2S5n. 

Acquisition of knowledge begins 
with the individual and concrete 
361. 

Addition, the Principle of 234. 

Adequacy of Propositions 55. 

Adjectives, their logical force 48. 

Affirmation, grounds of 102. 

Affirmative Judgments classify 
their subject 54, how related to 
Negative 61, do not distribute the 
Predicate 67, substitution of terms 
in 76. 

Agassiz Prof, view of Classification 
and Induction 312 n. 



Ai^drich's account of the Predica- 
bles 19 n. 

Algebra, a series of Methods of In- 
vestigation in Discrete Quantity 
234. 

Alternate Conceptions 15. 

Alternate Species 27, used as 
subjects 56, constitute coordinate 
terms in Disjunctive Judgments 
100. 

Amotion of a Proposition, what 
172 n. 

Ambiguous Middle what 189, vari- 
ous forms of 190. 

Ampere's Classification of the Sci- 
ences criticised 340. 

Analogous Spheres 20. 

Analogy 33 and 249 n., proved by 
Affirmative Premises in the 2d 
Figure 124, as a Method of In- 
vestigation 249, Aristotle's and 
Whately's definition of 249 n., 
stops short of an Induction 257, 
its use 257-259, argument from 
319, its value 320, as a means 
of removing antecedent objec- 
tions 321. 

Analysis, what 215, difierent kinds 
of 215, proximate and ultimate 
or last 216, must precede synthe- 
sis 218, as a Method of Investi- 
gation 243, of conceptions and of 



k 



412 



INDEX. 



things, logical and physical 243, 
certainty of its results 244 et seq^, 
enables us to see Implied proper- 
ties 248. 

Analytic Method of Teaching 362, 
based upon the Natural Classifi- 
cation 363. 

Analytic Judgments 203, do not 
add to our knowledge 203, a priori 
206. 

Antecedence not Causality, though 
implied in it 259, proved by In- 
duction 260. 

Antecedent in a Conditional Judg- 
ment 91, ground of the truth of 
the Consequent 171. 

Antecedents in Nature, simple and 
complex 264. 

Antecedent Probability and im- 
probability with reference to dif- 
ferent totalities 89. 

Antithetic Terms 41. 

Apodictic or Necessary Judgments 
60, their relation to the Assertives 
as used in Formula 63. 

Appeal to facts 303. 

Approach progressive 324. 

Arguivient analyzed 7, from Con- 
ceptions 281, from Principles 290, 
from Authority 293, from Facts 
303, by Induction 304, by Exam- 
ple 316, by Analogy 319, by con- 
currence of Circumstances and 
Testimony 322, by Progressive 
Approach 324, Argumentum ad Ig~ 
norantiam 326, from Exceptions 
330, ad Hominem 336, ad Verecun- 
diam 336, ad Invidiam 337, distin- 
guished from Assertion 374, and 
Artifices 374. 

Aristotle the founder of Logic 1, 
attributes its origin to Zeno 2, his 
Categories 34 71., his Dictum 124 n., 
his list of Sophisms or Fallacies 
184 7i., his tme Conclusion from 
false Premises 187 ?i., his defini- 
tion of Induction 249 n. and 
304 w., his Notions 311, Classifi- 
cation of the Sciences 339, Meta- 
basis 379 n. 

Arithmetic a scries of Methods of 



Investigation in Discrete Quan- 
tity 234. 

Article not used before words de- 
noting Genera 52. 

Artifices to be distinguished from 
Formula and from Fallacies 192, 
from Arguments 374. 

Arts, the Faculty of 339. 

Assertion to be distinguished from 
Argument 374. 

Assertive Judgments 61, their re- 
lation to the Formula 63. 

Authority proved by Testimony 
231, Arguments from 293, our 
only ground of proof in some 
cases 294. 

Average, a Method of Investigation 
237, its various uses 238, 239, 
240. 

Axioms 290 note, how proved 278. 

Bacon's Experimentum Crucis 273, 
Classification of the Sciences 340. 

Barbara, Syllogism in 119, all Syl- 
logisms whose names begin with 
B may be reduced to 127. 

Baroko 120, reducible to Barbara 
127, 128, to Ferio 129. 

Beautiful, the Idea of the, as de- 
termining Methods 199, its rela- 
tion to the Useful 201. 

Begging the Question, Fallacy of 
186. 

BoKARDO 121, may be reduced to 
Barbara 127, 129, to Darii 129. 

Botany cited as an illustration of the 
Progress of Scientific Classification 
358. 

Bramantip 122, may be reduced to 
Barbara 127, 128, peculiarity of 
in the resolution of Sorites 141. 

Butler Bishop, Method of in the 
Analogy 321, 334. 

Calculation, Methods of in Dis- 
crete Quantity 233. 

Calculus, a series of Investigations 
in Discrete Quantity 234. 

Camenes 122, may be reduced to 
Celarent 127. 



INDEX. 



413 



Camestres 120, may be reduced 
to Celarent 127. 

Categorematic, terms when said to 
be 13. 

Categorics 13, of Aristotle 34 w., 
of Kant 34 n. 

Categoric Judgments 44, Pure, 
Comparative, and Probable 45, 
make a Classification 50, simple 
and complex 77, Compound, Co 
pulative 80, Causal 81, Discretive 
81, Conditional 82, Disjunctive 82, 
Exceptive and Exclusive 83, Com- 
parative 84. 

Categorical Syllogisms include 
three Propositions and three 
Terms 108, names of Terms and 
Premises in 108, 109, number and 
names of 122, indirect conclusions 
of 123, conversion of 124, Modals 
in 131, Compound or Sorites 138, 
Compound Propositions in 149. 

Causal Propositions 81, are pro- 
perly Enthymemes 150, how com- 
pleted 150. 

Causality something more than 
Antecedence 259, not proved by 
Induction 260, three conditions 
required 261, often depends upon 
the Mode of the Substance 263, 
often depends upon the complex- 
ity of the Antecedent 264. 

Cause absolute 29, and efiect alter- 
nate conceptions 30, relative 30, 
primary and secondary 30, effi- 
cient, occasional, material, formal, 
final, and negative 30, transient, 
permanent, and immanent 32, in 
Nature only secondary 260, called 
also Instrumental 261, Substan- 
tial and Modal 259, must be a 
substance 261, causa vera and 
causa sufficiens 262, adequate and 
homogeneous 263, four kinds of 
words denoting Causes 264, when 
to be given in Instruction 365. 
Celarent 119, all Syllogisms begin- 
ning with C may be reduced to 1 27. 
Certainty absolute 211, physical 
212, moral 213, in regard to 
masses of men 213. 



Cesare 120, reduced to Celarent 

128. 
Chain Syllogism or Sorites 138. 
Chances favorable and unfavorable 
87, in the same and in difierent 
Events 165. 
Circumstances, facts regarded as 
215, argument from 322, its pro- 
per sphere 323. 
Class-conceptions what 205, of 
the Creative Mind the basis of 
Induction 306. 

Classification implied in all Cate- 
goric Judgments 50, Principle of 
extends to more than three grades 
51, based upon accidental proper- 
ties 53, become jests 54, Formula 
of 146, made at the second ob- 
servation 221, and a new one at 
the next 221, the basis of Induc- 
tion 250, the principle of changes 
in the progress of science 252, 
357, a new one required when the 
exceptions become numerous 256, 
not properly based upon variable 
properties 256, of the Sciences 338, 
Plato's, Aristotle's, and the Scho- 
lastic 339, Bacon's, Locke's, Cole- 
ridge's, and Ampere's 340, Comp- 
te's 341, a new one 342 et seq., 
character of the Primary 356, 
necessity for the transition from 
Natural to Scientific 357, test of 
the perfection of 357, 358, illus- 
trated from Botany 358. 

Cognition 7, 9, distinguished from 
Conception 10. 

Collective Terms distinguished 
from General 17, may not be pre- 
dicated of the individuals 18. 

CoMisiissiONS conveying authority 
how to be interpreted 300. 

Common Sense, a ground of belief 
294. 

Comparative Judgments 45, do 
not include the Subject in the 
Sphere of the Predicate 84, con- 
tain three terms 85, of seven va- 
rieties 84-87, conversion of 86, in 
Syllogisms 151. 

CoaiPARATivE Syllogisms, not the 



414 



mDEX. 



same as pure Categorlcals 151, 
simple comparatives 152, the con- 
ditions of their validity 154, in 
whicli intensity is regarded as 
cause 155, of manner, time, place, 
&c. 156. 

Comparisons, imply three terms 85, 
of equality and inequality, and of 
greater and of less intensity 85, 
of time, place, &c. 86. 

Composition, Fallacy of 190. 

Complex Propositions reducible to 
simple incomplex 81. 

Compound Categorical Proposi- 
tions reducible to simple complex 
81. 

Co^ipouND Conditionals 96, 171. 

Comprehended Sphere always the 
Subject 111. 

Comprehending Sphere always the 
Predicate 111. 

Comprehension of Terms 11. 

Comprehensive Quantity deter- 
mines the intensive 60, of three 
degrees 60. 

Comprehensiveness of terms ex- 
clusiveness of matter 51. 

Compte's Classification of the Sci- 
ences 341. 

Conception 7, 9, adequate and in- 
adequate 10, of Ideas, how made 
adequate 11, of the Impossible 12, 
the relations of 13, the sphere and 
matter of 14, matter determines 
the sphere 15, Alternate 15, dis- 
tinguished from facts 214, manner 
of passing from one mind to an- 
other 216, 347, Analysis of 244, 
cannot be conveyed from mind to 
mind as wholes 348, reconstructed 
by the person receiving it 349, 
none that cannot be denned 351, 
Ultimate and Primary 355, imply 
previous perceptions 356, made 
distinct by the Essentia, definite 
by the Differentia 366. 

Concessions a ground of proof 294. 

Conclusion, what 7, 307, no af- 
firmative in the 2d Figure 113, no 
universal in the 3d 114, quantity 
and quality of determined by the 



Premises 115, indirect 123, direct 
123, compound 149, true from 
false Premises, Aristotle's account 
of 187 n., when proved 280, as 
determining wholes in argumenta- 
tion 375. 

Concrete, knowledge begins with 
objects in the 361. 

Concrete Terms 14. 

Concurrence of facts or of testi- 
mony, what 322, its value 323. 

Conditional Judgments 44, imply 
categoric 45, three terms and two 
copulas 91, members of 91, depend 
upon the Sequence 92, compound- 
ed with Disjunctives 102. 

Conditional Modals 79, may be- 
come Differential 136. 

Conditional Propositions 82, 91, 
compound 96, continuous 96. 

Conditional Syllogisms, not all 
that contain conditional judg- 
ments are so 171, methods of 
completing 172, method for find- 
ing the Sequence 173, may be 
completed into a categorical 174, 
with four terms 174, compound 
174, continuous 175, with com- 
pound consequents or antecedents 
175. 

Conjecture, what 218. 

Conjugation of the Verb as an illus- 
tration of Definition 354. 

CoNNOTATivE Tcrms 14, how predi- 
cable 42. 

Consciousness, a means of Investi- 
gation 224. 

Consequent in conditional judg- 
ments 91, the denial of destroys 
the Antecedent 172. 

Construction, object and method 
of 347. 

Constructive Method with Condi- 
tionals 172. 

Contingent Matter 205, judg- 
ments in a posteriori 206, in all 
realities of being 209, how knowTi 
210, Analysis as a means of In- 
vestigation in 244. 

Continuous Conditionals 96. 

Continuous Quantity 22, limits 



nSTDEX. 



415 



and terms in 23, 39, axioms of 
152. 

CoNTEADiCTio in odjectis 375. 

Contradiction, principle of, a ground 
of affirmation 103. 

Contradictory Terms 41, how pre- 
dicate 42. 

Contradictory Judgments cannot 
both be false in the same matter 
70. 

Contraries, a means of Investiga- 
tion 250. 

Contrariety 33. 

CoNTRA-POSiTioN of Judgments 71, 
by means of Negatives 73. 

Contrary Judgments cannot both 
be true in the same matter 70. 

Contrary Terms 40, how predica- 
ble 42. 

Conversion of Propositions 74, sim- 
ply and by limitation 75, of 75, 
of Comparatives 86, of Syllo- 
gisms 124. 

CoNA^EYiNG words of, how to be in- 
terpreted 299. 

Coordinate Divisions 25, parts 26. 

Copula, affirmative and negative 7, 
its force 48, its effect in pure cate- 
goricals 49, its form 49, real and 
designed effect of 50. 

Copulative Propositions 80, maybe 
resolved into simple Propositions 
80, danger of their including er- 
ror 81. 

Counting, a method of Investiga- 
tion 234. 

Critic the, position occupied by 369. 

Criticism, principles of, the same 
as those of Construction 369, 
starting point of 370. 

Damascene, St. John, on Analysis 
215 w. 

Darii 119. 

Datisi 121, may be reduced to Da- 
rii 127. 

Deduction, compared with Induc- 
tion 276 w., as a method of Proof 
290, the method of appUcation of 
Sciences 291, and of completing 
Sciences 292. 



Deductive Judgments, how differ- 
ent from Intuitive 106. 

Definition 33, may be predicated 
of any object 55, used instead of 
the term 131, analyzes conceptions 
349, when adequate 349, 353, 
verbal and real 350, may be 
given to all conceptions 351, 
some difficulties noted 352, Ac- 
cidental, Physical, and Meta- 
physical 353, negative, what 353 
7^., the conjugation of verbs a 
definition 354, may need to be 
defined 355, must always refer 
to the natural classification 359, 
use of negative in instructioij 
365 n. 

Demonstration, popular and strict 
senses of the word 281, from the 
force of terms 282, based on ety- 
mology 283, not used in Contingent 
Matter 284, 287, the basis of all 
Sciences 285, 290, gives Universal 
Conclusions from Individual Pre- 
mises 286, based upon Hypothe- 
ses 288. 

Demoniacal Possessions, how prov- 
able 227 n. 

Description, what 34, as a means 
of conveying conceptions 351, does 
not furnish the matter for the con- 
ception 355. 

Destructive Method with Condi- 
tionals 172. 

Devey's Logic cited 292 n. 

Diagrams in Mathematics as repre- 
senting conceptions 207. 

Dictionaries a Testimony to the 
meaning of words 232, gives ver- 
bal definitions. 

Dictum of Aristotle 124 w., of Lam- 
bert 125 n. 

Difference in kind and in degree 
32. 

Differentia must bear some rela- 
tion to the Essentia 51, may be 
merely relative Properties 351 n., 
the same in different genera con- 
stitute Recurring Species 359, 
always necessary in Instruction 
364. 



416 



INDEX, 



Differential Modals 78, may be 
converted into Conditional 136. 

DiLEiiMA 102, seldom needs comple- 
tion 179, its various forms 179- 
181. 

DiMARis 122, may be reduced to 
Darii 127. 

DisAMis 121, may be reduced to 
Darii 127. 

Discrete Quantity 22, terms and 
limits of 22, applied to Logical 
and Continuous 23, terms in 38, 
gives validity to syllogisms other- 
wise invalid 152, two axioms of 
157, applied to continuous in cate- 
gorical Syllogisms 158, affords no 
distributed terms 159, its effect 
Avben applied to one Premise only 
162. 

Discretive Propositions 81, in Syl- 
logisms 150. 

Disjunctive Judgments 4:4, imply 
categoric 1:5, depend upon the Ex- 
cluded Middle 97, with four terms 
101, compounded with condition- 
als 102, convertible into condi- 
tionals 102, comprehensive and 
divisive 175. 

Disjunctive Propositions 82. 

Disjunctive Syllogisms 175, com- 
prehensive and divisive 176, Syl- 
logisms not always disjunctive 
when there is a disjunctive Pre- 
mise 176, the Major Premise dis- 
junctive 177, how completed mo- 
dus tollente poneris, and ponente tol- 
lens 177, with more than two mem- 
bers 178, divisive, how completed 
178. 

Disparate Parts 26, do not consti- 
tute an Excluded Middle 100. 

Distributed Terms 40, in judg- 
ments 64, by nature, by signs ^^^ 
by position 67. 

Division 21, of three kinds 24, prin- 
ciple of 25, coordinate and subor- 
dinate 26, canons of 28, fallacy 
of 190, numerical 23(>, of general 
subject in teaching 3 (JO, into coor- 
dinate parts if possible 361, into 
alternate species 36 1 . 



Divisive Judgments 175. 
Divisive Principle 25. 
Divinity, the Faculty of, in the Uni- 
versities 339. 

Each, a sign of a distributed subject 
in a Proposition QQ. 

Edicts restraining liberty, how to 
be interpreted 300. 

Effect and Cause alternate concep- 
tions 30, immediate and remote, 
direct and accidental, designed 
and undesigned 32, investigation 
of 271, 273, when to be given as 
an element of Instruction 365. 

Elimination, when practicable 265, 
depends upon four axioms 266, 
first Method of Elimination 267, 
second and third 268, fourth 269, 
fifth 271. 

End, Method supposes one, but does 
not furnish it 196, determines 
the selection of matter in Instruc- 
tion 367, 369, in determining 
wholes 375. 

Enthymemes, what 142, of four kinds 
143, with three terms may be 
completed into Syllogisms 143, 
with four terms, completed into 
Sorites 144, may be stated as Con- 
ditionals 173. 

Epichirema 148. 

Epi-syllogism 148. 

Equality, comparisons of 85, mean- 
ing of in Algebra 157 w. 

Essence of an object 16, different 
senses of the word 16 w. 

Essentia of a Genus 17, always ne- 
cessary in Instruction 364, makes 
the conception distinct 366. 

Ethnology, cited as an illustration 
of the principle of classification 
357. 

Exact Sciences, what and why so 
called 342 n. 

ExA.^iPLE, argument from 316, an 
induction from a single fact 318, 
W'hately's view of the reasoning 
from 318 n.^ chiefly confined to 
moral matter 318, its value 319. 

Exceptions, becoming numerous 



INDEX. 



417 



indicate a faulty classification 256, 
as a means of refutation 329. 

Exceptional Modals 78. 

Exceptive Propositions 83, easily 
converted into Exclusives 83, in 
Syllogisms 151. 

Excluded Middle, what 97, be- 
tween contradictories and subcon- 
traries 97, a ground of affirma- 
tion 104. 

Exclusion, as a Method of Investi- 
gation 240, two forms 241, its 
uses 241, 242. 

Exclusive Modals 79. 

Exclusive Propositions 83, easily 
converted into Exceptives 83, in 
Syllogisms 151. 

Experiment, as a means of investi- 
gation 224. 

EXPERIMENTUM CRUCIS 273. 

ICxpLicATivE Modals 78. 

ExposiTA, what 71. 

Extension, not predicable of time 
and space 23 w., incompatible 
with infinite 23 n. 

Extremes, in a categorical Syllo- 
gism 108. 

Event, in the calculation of chances 



what 165, 
fact 214. 



distinguished 



from 



Facts defined 213, distinguished from 
Events, Conceptions, and Ideas 
214, phantasms and fancies 215, 
as circumstances 215, first known 
as complex wholes 215, distin- 
guished from inference 230, how 
used in Arguments 303, distin- 
guished from laws 303. 

Faculties, University distribution 
of 339. 

Fallacies, defined and classified 182, 
in form, in matter, in diction, and 
extra-logical 183, effect of 183, 
Aristotle's list of them 184 7^., 
Ignoratio Elenchi 185, Petitio Prin- 
cipii 186, Ambiguous Middle 189, 
Division and Compe^sition 190, of 
Accidents and of Quid 191, post hoc 
ergo propter hoc 259 7^., Contradic- 
tio in adjectis 375, Metabasis 379 n. 



Fancies, 

215. 
Faults 



distinguished 



from facts 



183. 



distinguished from Fallacies 



18* 



Felapton 121, reduced to Ferio 128. 

Fe-rio 119, all Syllogisms beginning 
with F may be reduced to 127. 

Fesapo 121, may be reduced to Fe- 
rio 127. 

Festino 120, may be reduced to Fe- 
rio 127. 

Figure, of Syllogisms what, and 
the differentia of each 110, the 
4th Figure valid, though unnatu- 
ral and inelegant 111, the 1st and 
4th depend upon the same prin- 
ciple 112, the 2d 113, the 3d 113, 
the 1st has six valid and four use- 
ful Syllogisms 119, the 2d has 
also six valid and four useful 120, 
the 3d Figure has six 121, the 4tli 
Figure has five 121, the 2d Figure 
proves Analogy by affirmative Pre- 
mises 124, the pecuHarities of 
omitted in general discussion 130. 

Final Causes, what 31, a basis for 
Induction 313, imply a Creative 
Intelligence 314. 

Form, distinct from the matter 5, 
of judgments 44. 

Formal Properties 210, imply Mo- 
dal 222, an accidental may be 
formal 222, the basis of classifica- 
tion for the purpose of Induction 
24^, 250, the basis of Analogy as 
a Method of Investigation 258. 

Formula 7, of Classification and In- 
duction 146, of the cumulative 
Argument 147. 

Fresison 122, reduced to Ferio 128. 

General Subject in instruction, its 
division 360. 

General Terms, how distinguished 
from Collective 17. 

Genus, a sphere 17, predicable in 
Quid 19 n.j Summum and Proxi- 
mate 20, what may be predicated 
of 55. 

Giving and Conveying words of, 
how to be interpreted 299. 



418 



INDEX. 



GocLENiAN Sorites 140, 138 n. 
Good, tlie Idea of, as determining 
Methods 199. 

Hamilton Sir William, Ms new Me- 
thod of Notation and Quantifica- 
tion 67 n., see also the Preface, his 
Unfigured Syllogism 111, his opia 
ion of Induction 308 n. 

History, the facts of, in what sense 
a field for Induction 311. 

Hypothesis, what 218, use of in 
investigating modal properties 223, 
in general 226, used in Demon- 
stration 288, legitimate use of in 
continorent matter 289. 

Hypothetical Judgments, why so 
called 45. 

Ideas, furnished hy the Reason 11, 
which determine Methods 198, dis- 
tinguished from facts 214, how 
transferred from one mind to an- 
other 347, of Totality 370 et seq. 

Identical Judgments 48. 

Identity of objects perceived 9, 
explained 33, principle of, a ground 
of affirmation 103. 

Ignoratio Elenchi not a mistake 
in Logic 185, why so called 185, 
when most likely to occur, and 
the effect of 185. 

Illicit Process of the Minor and of 
the Major 115, 116. 

Immediate Inference explained 69. 

Immortality of the Soul, Bp. But- 
ler's method of reasoning about 
321, 334. 

Impertinent matter always to be 
rejected 367. 

Implied Properties 209, learned 
by Observation 222, by Measure- 
ment 233, by Analysis 248. 

Impression often made without ar- 
gument or Instruction 373. 

Improbability, what 88, not the 
same as the probability of the op- 
posite 89, nor as the mere want of 
probability 90. 

Indiffkrkntia, what properties so 
called 20. 



Indirect Conclusion in pure cate- 
gorical Syllogisms 123, must be 
used instead of the direct in cer- 
tain cases 141. 

Individuals, what 19, absolute and 
relative 27, necessarily included in 
a Species 53, what may be predi- 
cated of 55. 

Individual Judgments 60, formed 
before Universal 330 n. 

Indefinite Judgments, what 61, 
how related to the Negative 63. 

Induction, the Formula of 146, as a 
Method of Investigation 249, Aris- 
totle's definition of 249 y^., three 
classes of cases 251, three steps in 
the first class 253, second class 254, 
third 255, compared with Deduc- 
tion 276 w., as a Method of Proof 
303, implies the Uniformity of Na- 
ture 304, and a Creative Mind 306, 
completed into Syllogism 308, be- 
longs to physical matter 309, does 
not extend to accidental proper- 
ties 310, approaches Demonstra- 
tion 311, limited to properties im- 
plied in the original class-concep- 
tion 311, by means of Final Causes 
313, imphes an Intelligent Creator 
315, how far applicable 316. 

Inequality, comparisons of 85. 

Inference Immediate, from subal- 
terns 70, from universals 70, from 
contradictories 70, from Exposita 
by permutation 76, by the sub- 
stitution of terms 77, from judg- 
ments in Necessary Matter 211. 

Infima Species 20. 

Infiniit:, a term in Logical Quantity 
23, incompatible with extension 
23 71., meaning of the word 36 «., 
in Discrete Quantity 39, as a Pre- 
dicate, how proved 279. 

Intensity, regarded as a cause 86, 
in Syllogisms 155. 

Intensive Quantity, determined by 
the Comprehensive 60. 

Interpretation, necessity for 297, 
Rules of 297. 

Intuitive Judgments 106. 

Instruction, Methods of, how far 



INDEX. 



419 



belong to Rhetoric 347, determin- 
ed by the conditions of conveying 
conceptions 348, two Methods of 
362, division of matter in refer- 
ence to 364, order in 366, End 
as determining the selection and 
order of the matter 367 et seq. 
Investigation the method of find- 
ing Predicates to given subjects 
219, of accidental and modal pro- 
perties 222, of miplied 223, Modal 
by means of hypotheses 223, be- 
gins with individual objects 225, 
de novo and following another 226, 
use of hypotheses in 226, in Dis- 
crete and Continuous Quantity 
232, by Average 237, by Exclusion 
or Abscissio 240, by Analysis 243, 
by Induction 249, of Causes by 
Elimination 259, leads to a first 
and absolute Cause 260. 



Jests are but ludicrous classifica- 
tions 54. 

Judgment 7, defined 43, form and 
matter of 44," scope of 44, of three 
kinds 44, Categoric, Conditional, 
and Disjunctive 44, Hypothetical 
45, Comparative and Probable 45, 
formation of 47, resolvable into 
terms and terms with modals 47, 
Identical 48, Individual, Parti- 
cular, and Universal 60, quality 
of Affirmative, Negative, and In- 
definite 61, Modality of, Problem- 
atic, Assertive, and Necessary 61, 
four cardinal A, E, I, and O 62, 
Negative with undistributed Pre- 
dicates 67 n., every judgment im- 
plies another 69, opposition of 70, 
Permutation or contra-position of 
71, Comparative 84, Probable 87, 
Conditional 91, Disjunctive 97, 
Intuitive and Deductive 106, An- 
alytic and Synthetic 203, in Ne- 
cessary Matter 205, a priori and 
a posteriori 206, w^hen incapable 
of proof 277, Individual before the 
Universal 330 ?i.. Universal ex ne- 
cessitate rei and de facto 330 », ] 



Kant, his Categories 34 w., his Syl- 
logisms of the Understanding 69. 

Lambert, his dicta of the Figures 
124 n. 

Later-first, a fault in Method 197. 

Latimer Bp., his exposition of the 
Fallacy of post hoc ergo propter hoc 
259 n. 

Law, the Faculty of 339. 

Laws restraining liberty, how to be 
interpreted 300, distinguished from 
facts 303. 

Length, a secondary property 23 n. 

Liberty, laws restraining, how to 
be interpreted 300. 

Limits, doctrine of, in Progressive 
Approach 325. 

Loci, what 219 7^. 

Locke's classification of the Sci- 
ences 340. 

Logic defined 1, later than Philoso- 
phy 1, its necessity 2, holds the 
second place in Philosophy 3, the 
science of deductive tliinking 3, a 
Science 3, in what sense an Art 3, 
its relation to Rhetoric and Dia- 
lectics 4, 347, not to be regarded 
as a means of discovery 4, Formal 
or Analytic 5, Rational 5, AppHed 
6, presupposes a knowledge of the 
Matter 6, proposes no new way of 
reasoning, but explains the old 6. 

Logical Division 25. 

Logical Quantity 22, limits and 
terms in 23, 39, of three dimen- 
sions 59. 

Major Premise in categorical Syl- 
logisms, what 108, called the 
" Principle," not usually expressed 
in Induction 275 n. 

Major Term .by nature and by loca- 
tion 108, change of its Modal 135. 

Material Properties 209. 

Mathematics deals with Concep- 
tions only 244 and note. 

Matter of Arguments 5, of a Con- 
ception 14, determines its Sphere 
15, of a Genus and of a Species 21, 
accidental 21, of judgments 44, 



420 



INDEX. 



of conditional judgments 91, as 
determining Methods 202, Neces- 
sary 204, Contingent 205, Neces- 
sary and Contingent in the same 
Conception 206, Moral 212, of a 
Conception divided with reference 
to the order of treatment 364, im- 
pertinent to be rejected 367, new 
matter not to he introduced by the 
critic 374. 

Maxims 219 ti., how distinguished 
from Axioms 290 n. 

Measurement, as a Method of In- 
vestigation 232, a means of inves- 
tigating imphed Properties 233. 

Mediate Inference, always imphes 
a Middle Term 107. 

Medicine, Faculty of 339. 

Members of conditional judgments 
91. 

Memory depends upon Method 367. 

Metabasis, fault of 379 n. 

Metaphysics, one branch of Philo- 
sophy 3. 

Method, included in Logic 1, distin- 
guished from the Matter and the 
Form of Arguments 5, Method in 
general 194, gives unity and im- 
plies capacity 195, order imphed 
in 196, the Ideas that determine 
198, Matter as determining 202, 
of Investigation 219, Observation 
and Testimony 223^ Measurement 
232, Counting and Calculation 234, 
in Mathematics 234, Average and 
Exclusion 237, Analysis 243, In- 
duction and Analogy 249, of find- 
ing causes (Elimination) 259, of 
Proof 275, Demonstration 281, 
Deduction 290, of appeal to Au- 
thority 293, of appeal to Facts 303, 
Induction 304, by Example 316, 
by Analogy 319, by concurrence 
of circumstances 322, of Progres- 
sive Approach 324^ of Refutation 
328, Direct 329, Indirect 333, In- 
direct Methods always imply Di- 
rect Methods to the same result 
335, Personal 336, of Uhetoric 
determined by the Idea of the 
Useful 347, of Instruction for the 



most part Rhetorical 347, Ana- 
lytic and Scientific in teaching 
359, 362, of Criticism 369, how 
criticised 372. 

Middle Term, its office in Syllo- 
gisms 107, 110, must be once dis- 
tributed 114, the law of chancrino; 
its Modal 134, may be stated indi- 
vidually 146, the necessity for so 
stating it 147, may be a disjunctive 
judgment in one Premise 176, am- 
biguity of 189. 

Mill denies the reality of necessary 
matter 205 »., opinion on the Uni- 
formity of Nature 305 n. 

Minor Premise in Categorical Syl- 
logisms 108, called " the case," 
" the example," or " instance," 
109. 

Minor Term, by nature and by po- 
sition 108, the real subject of the 
Syllogism 108, change of its Mo- 
dal 135. 

Modal Properties 210, investi- 
gated by observation 222, by 
means of Formal Properties 223, 
225, by Induction 251, 252, In- 
duction commencing with 254. 

Modality of Judgments, three va- 
rieties of 61. 

MoDALS 77, Explicative and Differ- 
ential 78, Exceptional, Exclusive, 
Conditional, and Proteusive 79, 
when omitted and when inserted 
in the course of an argument 132— 
135, may be transferred from one 
term to the other 136, protensive 
ModaL in Syllogisms 13 T. 

MoL'Ls tullejhs and pomns 172, tollente 
poneiis and ponente tollens 111, po~ 
nente iol'ens^ when valid in disjunc- 
tive Syllogisms 178. 

Moods ot SyUogisms 115, not all 
valid 115, 116. 

Moral Matter 212, does not admit 
of Induction 309. 

Multiplication, a Method of Addi- 
tion 236. 

Name of any thing may be predi- 
cated of that thin«y 55, 



INDKX. 



421 



Nature, uniformity of, what 304, 
how used in Induction 308, ab- 
normal cases in 316. 

Necessary or Apodictic Judgments 
60. 

Necessary Matter of the subject 
included in the scope of the Judg- 
ment 58, in relation to Method 
204, Mill and Whewell's contro- 
versy about 205 ^^., and contin- 
gent in the same conception 206, 
Analysis of 245. 

Necessity, Physical and Moral 212. 

Negative Definitions, what 353 n.^ 
use of in Instruction 365 n. 

Negattv^e Judgments, what 61, al- 
ways distribute the Predicate 67 
and note^ substitution of terms in 
76. 

Negative Terms, complements of 
the Positive 36, but few 37, dis- 
tinction between them and Priva- 
tive unimportant 37, in Discrete 
Quantity 38, in Continuous Quan- 
tity 39. 

NoN TALI PRO TALI, Fallacy of 188. 

NoN VERA PRO VERA, Fallacy of 
188. 

Numerals 38. 

Numerical Division 24. 



Oaths, how to be interpreted 299. 

Obiter Dicta, how interpreted 302. 

Objects of Thought, possible, im- 
possible, and real 12, perceived 
as wholes 47, classified as soon as 
we have more than one 221. 

Observation, a Method of Investi- 
gation 220, difference between 
and Testimony 221, as a Method 
of Investigation 223. 

Omission, as an element of Method 
198, not testimony 229, in In- 
struction 368. 

Opinion, as distinguished from Truth 
217, not provable by Testimony 
296. 

Opposition of Terms, relative, con- 
trary, subcontrary, and contradic- 
tory 41. 



Order, as an element of Method 
194, 196, five Canons of 197, of 
treatment in Instruction 361 et seq. 

Ordinals 38. 

OsTENSiVE Reduction of Syllogisms 
128. 



Pantheism, results from denying 
the limited nature of Positive 
Spheres 36 w. 

Pappus' account of Mathematical 
Analysis 21 o n. 

Parables, how to be interpreted 
301. 

Particular Judgments 60. 

Particular Affirmative Judg- 
ments distribute none of their 
terms 68. 

Particular Negative Judgments 
distribute their Predicate 68. 

Parts, Disparate 26, assumed as 
wholes 26, subordinate 26, to be 
criticized only in relation to their 
wholes 372. 

Perception, an instantaneous act 9. 

Permutation of Judgments, what 
71, by means of Negatives 73. 

Personal Refutations 336. 

Petitio Principii, what 186, why 
so called 186, several forms of 
187, 188. 

Philosophy before Logic 1, neces- 
sitated it 1, divided into three 
branches 2. 

Physical Division 24. 

Plato divided Philosophy into three 
branches, 2, 338, his use of the 
word ^'Ideas'' 311. 

Plausible, the Idea of, as deter- 
mining Methods 199 n. 

Pleasure, the Idea of, as determin- 
incr Methods 199. 

Porphyry, his account of the Pre- 
dicables 17 n., 19 n. 

Post hoc ergo propter hoc, Fal- 
lacy of 259 n. 

Posit to, a Proposition, what 172 n. 

Positive Terms 35, imply nega- 
tives 36, in Discrete Quantity 38, 
in Continuous Quantity 39. 



422 



INDEX. 



Predicables 13, as reckoned by 
Porphyry 17 n,^ Aldrich's account 
of 19 n. 

Predicate 7, usually placed after 
the Copula 46, used with refer- 
ence to the matter of the Con- 
ception 47, what words may he so 
used 47, used for the matter of its 
Conception 50, must include the 
necessary matter of the Subject 
58, matter expressed in 224, 
found by the Methods of Investi- 
gation 219. 

Premises in Categorical Syllogisms 
108, both negative 112, the rela- 
tion of their quantity and quality 
to rest of the Conclusion 108-117, 
affirmative give no negative Con- 
clusion 117, their order unimport- 
ant 126, one sometimes suppressed 
142, a universal may not be sup- 
plied when a particular will an- 
swer 143, compound in Syllogisms 
149, Premises unduly assumed, 
various forms of 188, may be con- 
clusions of preceding premises 280, 
to a Conclusion, whatever is ne- 
cessary to it 308. 

Primary Properties, their relation 
to the Secondary 23 w. 

Privative Terms complements of 
the Positive 36, used instead of 
Negatives 73. 

Probability, its nature and the 
method of estimating it 87, and 
improbability, complements of 
each other in unity 88, antece- 
dent 89, exact value of 89, ap- 
proximate 90, general and special 
91, dependent 162, in the same 
and different events 165, Alge- 
braic formula for its computation 
170 «. 

Probable Judgments 45, 87. 

Probable Syllogisms 157, method 
of notation in 160, how many at 
least 160, at most 161, when the 
probabilities are dependent upon 
each other 162, when they are 
independent 165, methods of cal- 
culatmg 168, 169. 



Problematic Judgments 60, not 

used in the Formulae 63. 

Progressive Approach, the argu- 
ment of 324, first class of cases 
324, second class 325, often more 
satisfactory than Demonstration 
326. 

Proof, how different from Investi- 
gation 275, Direct 276, requires 
two conditions 277, Indirect 278, 
of Negative Predicates 278, of 
Negative Copulas 279, Demon- 
stration 281, Deduction 290. 

Properties, what 13, belong to 
more than one substance 13, Es- 
sentia 17, Differentia 18, Acci- 
dental 19, when called Qualities 
19 ?^., separable, inseparable, and 
individual 19, as primary and 
secondary 23 «., material and im- 
pHed 209, formal, modal, and va- 
riable 210, not distinguished into 
kind at the first observation but 
at the second 221, Formal first 
distinguished 222, Formal and 
Implied not distinguished by In- 
vestigation 222, Implied learned 
by measurement 233, by analysis 
248, of classes investigated by 
Induction 251, by Analogy 257. 

Propositions in an argument 7, 
contain two terms and a copula 
46, permutation of 71, 73, con- 
version of 74, simple and complex 
77, Compound, Express, and Im- 
plied 80, with Negative Predi- 
cates, how proved 278. 

Protensive Modals 79, their effect 
upon the Formula 136. 

Protensive Quantity 59. 

Pro-syllogisms 148. 

Psychology, a branch of Philoso- 
phy 2, some knowledge of requi- 
site in Logic 8. 



Qua, as indicative of alternate con- 
ceptions h% n. 
QuADRiviuM the, what 339. 
Quale, predication in 19 ;». 
Qualequid, predication in 19 n. 



INDEX. 



423 



Qualities, properties when so called 
Idn. 

Quality of Terms 34, of Judgments 
61, of Propositions changed by 
means of Negatives. 

Quantity, what 21, of three kinds. 
Logical, Continuous, and Discrete 
22, of terms 38, of judgments 59, 
of three dimensions 59, and three 
degrees 60, in conditional judg- 
ments 96, when to be given in 
Instruction 364. 

Question distinguished from the 
judgment 43, its relation to the 
Conclusion 109, mistaking the, 
fallacy of 185, begging the, fallacy 
of 186. 

Quid, predication in 19 n., (dictum 
secundum quid ad dictum simpli- 
citer) fallacy of 191. 



Kealities of Being and of Truth, 
how distinguished 12. 

Reasoning from Cause to Effect 
271, called also reasoning a priori 
271 ?i., from Effect to Cause 272. 
See Arguments. 

Recurring Species 359. 

Reductio ad Absurdum, as a Me- 
thod of Refutation 333. 

Reductio ad Impossibile 128, may 
be applied to all Syllogisms 129. 

Reduction of Syllogisms 127, os- 
tensive and ad impossibile 128. 

Refutation 328, three Methods 329, 
Direct 329, by Exception 329, of 
a Particular Judgment 330, of the 
reasoning instead of the Proposi- 
tion 331, Indirect 333, Personal 
336. 

Relative Judgments 45. 

Relative Terms of two kinds 40, 
imply and explain each other 
40. 

Religion, Method of Investigation 
in 231, proof in Matters of 293. 

Remembering, ease of, depends upon 
Method in Instruction 367. 

Residual Phenomenon 269, how to 
be disposed of 270. 



Rhetoric, its Methods determined 
by the Idea of the Useful 347. 

Scholastic classification of the Sci- 
ences 339. 

Sciences become more deductive as 
they advance 292, classifications 
of 338. 

Scope of Judgments 44, what pro- 
perties of the Subject included in 
58. 

Secondary Properties, their relation 
to Primary 23 n. 

Senses, the external, as Means of 
Investigation 224. 

Separable Accidents 19, not in- 
cluded in the Scope of a Judg- 
ment 58. 

Sequence in Conditional Judgments 
92, may be stated as a Categorical 
Proposition 92, of various kinds 
92-94, complex Sequence 94-95. 

Similarity 33. 

^' Some" not always indicative of 
an undistributed Term 64. 

Sophisms or Fallacies, Aristotle's 
list of 184 n., of Achilles and the 
Tortoise 235 n. 

Sorites, the usual form of 138, the 
Goclenian 138 7^., may be made 
from any Syllogism 139, resolv- 
able into Syllogisms 140, cautions 
m regard to their formation 139. 

Species, what 18, predicates in quid 
19 n., Infima 20, what may be 
predicated of 21, 55, parts of a 
Logical Division 27, Alternate 27, 
Recurring 359. 

Specific Terms 35, distributed 40. 

Spendthrift's Fallacy 191, rather 
a fault in criticism 370. 

Sphere of Conceptions 14, deter- 
mined by the Matter 15, Coinci- 
dent and Opposite 19, Analogous 
20, of positive, negative, and pri- 
vative terms 36, 37. 

Stewart Dugald, his opinion of the 
classification of the Sciences 340. 

Subaltern Genera and Species 20, 
Judgments 70, inferences from 
70. 



424 



INDEX. 



SUBCONTRARY JUDGMENTS 70, Hiaj 

both be true in the same matter, 
but not both false 71. 

SuBCONTKARY Terms 41, how pre- 
dicable 42. 

Subject 7, placed before the Copula 
46, used in reference to the sphere 
of the Conception 47, what words 
may be subject 47, used with re- 
ference to its sphere 50, classified 
in all affirmative judgments 54, 
distributed in universal judgments 
68, given by its sphere or by its 
matter 220, general and individual 
in Instruction 360. 

SxJBORDiNATE Divisions 26, parts 26. 

Substance, what 13, must have se- 
veral properties 13. 

Substitution of Terms in affirmative 
propositions 76, in negative 77. 

Subtraction, the principle of 236. 

Sufficient Reason, a ground of 
affirmation 103. 

Syllogism analyzed 7, divided into 
classes 106, pure categoricals 110, 
Canons testing the validity of 117, 
number and names of those that 
are valid and useful 122, their 
names indicative of the means of 
their conversion 126, complex ca- 
tegorical 131, pro tensive modals 
in 136, compound or Sorites 138, 
any Syllogism may be expanded 
into a Sorites 139, of Modals in 
131, the effect of protensive quan- 
tity upon 136, compound proposi- 
tions in 149, comparative 151, 
probable 157, conditional 170, 
disjunctive 175, not a Petitio Prin- 
cipii 186 and note, material and 
formal 378 n. 

Syllogisms of the Understanding 
69. 

Synonymous Terms 35, may be 
predicated of each other 55. 

Synthesis, what 216. 

Synthetic Judgments, what 203, 
a priori and a posteriori 206. 

Synthetic Method of* Teaching 359, 
362, why preferable 362, based on 
scientific classification 363. 



System, what 217. 

Technical Terms, how interpreted 
298. 

Terms 9, predicable 13, acategore- 
matic 13, concrete 14, abstract 14, 
denotative and connotative 14, 
comprehension and intension of 
14, essential and modal 17, gene- 
ral and collective 17, matter of 21, 
synonymous, equipollent, ambi- 
guous, incompatible, and positive 
35, negative and privative 36, in 
discrete quantity 38, in continu- 
ous quantity 39, in logical quan- 
tity 39, distributed and undistri- 
buted 40, their opposition 40, re- 
latives and correlatives 41, anti- 
thetic 41, contrary and sub-con- 
ti*ary 41, contradictory 41, in a 
proposition 46, importance of their 
quantity 59, distribution of, in 
judgments 64, distributed by na- 
ture 65, by signs 65, by position 
67, substitution of in affirmative 
propositions 76, in negative 77, 
in comparative judgments 85, in 
conditional 91, in disjunctive judg- 
ments 98, in a categorical syllo- 
gism 108, definitions used for 131, 
the modal of one transferred to 
another 136, denoting causes 264, 
force of, as a basis for demonstra- 
tion 282, criticism of 375. 

Testimony distinguished from Ob- 
servation 221, of two kinds 226, 
tests of its value 227, 228, 229, 
must be positive 229, negative, of 
what force 230, in necessary, phy- 
sical, and moral matter 231, to 
matters resting on authority 231, 
resolvable into observation and 
authority 280, legitimate use of, 
in Natural Sciences 295, regarded 
as a fact 322. 

Theology, Methods of Investiga- 
tion in 231, of Proof in 293. 

Theory, what 217, may be several 
for the same facts 217. 

Thinking, a primary property of 
mind 23 n. 



INDEX. 



425 



Thompson, his Outline of the Laws 
of Thought, quoted as of teaching 
an unfigured Syllogism 111. 

Titles, alternate conceptions of 
subjects 57. 

Topics, what 219 w. 

Totality, absolute and assumed 88, 
the idea of, an element of Criti- 
cism 370. 

Tkicks of Rhetoric, defined 192, to 
be distinguished from Argument 
in Criticism 374. 

TriyiUxM the, what 339. 

True, the Idea of the, as determin- 
ing Method 199. 

Truth, when a proposition is so 
called 217, absolute proved only 
by Demonstration 325. 



Undistributed Middle, Fallacy of 
114. 

Undistributed Terms 40, their re- 
lation to Judgments 64-69. 

Unfigured Syllogism 111. 

Uniformity of Nature, what 307, 
how used in Induction 308. 

Universal Judgments 60. 

University distribution of the Sci- 
ences and Faculties 339. 

Useful, the Idea of, determining 
Methods 199, relation to the 
Beautiful 201, determines the 
Methods of Rhetoric 347. 

*'T(rT€pov irpooToy, a fault in Method 
197. 

Usus Loquendi as a guide in Inter- 
pretation 298. 



Validity of Syllogisms, Canons de- 
termining the 117. 

Variable Properties 210, may 
become material or formal 210, 
not properly the basis of classifi- 
cation 256. 

Volney's '^ Ruins," cited as an ex^ 
ample of fault in Method 333. 

Wells Dr., his discovery of the cause 
of Dew 271. 

Whately Archbp. his account of 
Analogy 249 n., his account of 
reasoning a prion 271 n., from 
Example 318 n., his " Spend- 
thrift's " fallacy 371. 

Whewell Prof., his controversy 
with Mill concerning Necessarv 
Matter 205 n. 

Whole, the Idea of, necessary to 
Criticism 370, by what deter- 
mined 371. 

Wholes of three kinds 21, as Me- 
thods 372, in Arguments how 
determined 375, in Investigation 
and Construction 375. 

Witnesses, their character and po- 
sition as affecting the value of 
their testimony 226. 

Words denoting Genera used with- 
out the article 52. 



Zeno the Eleatic, the inventor of 

Logic 2. 
Zoology, cited as an illustration of 

the two Methods of Teaching 

363 n. 



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EXPOSITION OF THE GRAMMATICAL STRUCTURE OP 
THE ENGLISH LANGUAGE. 

BY JOHN MULLIGAN, A M. 

Large 12mo. 574 pages. $1 50 

This work is a comprehensive and complete system o English 
Grammar, embracing not only all that has been developed by the later 
{)liilologist9, but also the results of years of study and research on the 
part of its author. One great advantage of this book is its admirable 
arrangement. Instead of proceeding at once to the dry details which 
are distasteful and discouraging to the pupil, Mr. M. commences by 
viewing the sentence as a whole, analyzing it into its proper parts, and 
exhibiting their connection ; and, after having thus parsed the sentence 
logically, proceeds to consider the individual words that compose it, in 
all their grammatical relations. This is the natural order ; and expe- 
rience proves that the arrangement here followed not only imparts 
additional interest to the subject, but gives the pupil a much clearer 
insight into it, and greatly facilitates his progress. 

From Dk. James W. Alexander. 

" I thank you for the opportunity of perusing your work on the structure of toe 
English language. It strikes me as being one of the most valuable contributions to this 
important branch of literature. The mode of investigation is so unlike what appears 
In our ordinary compilations, the reasoning is so sound, and the results are so satisfac- 
tory and so conformable to the genius and great authorities of our mother tongue, that 
I propose to recur to it again and again." 

Extract from aletter from E. C. Benedict, Esq., President of the Board of Educa- 
tion of the City of New York. 

" I have often thought our language needed some work in which the principles of 
grammatical science and of the structure of the language, philosophically considered, 
were developed and applied to influence and control the usus and consuedo of Horace 
and Quintilian, which seem to me to have been too often the principal source of sole- 
cisms, irregularity and corruption. In this point of view, I consider your work a vala- 
able and appropriate addition to the works on the language." 

From Wm. Hokace Webster, President of the Free Academy^ New York. 

"The exposition of the grammatical structure of the English language by Professtir 
Mulligan, of this city, is a work, in my opinion, of great merit, and well calculated tc 
impart a thorough and critical knowledge of the grammar of the English .anguage. 

" No earnest English student can fail to profit by the study of tliis treatise, yet it Is 
designed more parti culary for minds somewhat maturer, and for pupils who are capabl« 
v\d have a desire, to comprehend the principles and learn tlu- philosophy of their own 
toL^ne.'" 



D. APPLE TON Sr CO., PUBLISHERS 



DICTlOlSrARY OF THE ENGLISH LANGUAGE 

BY ALEXANDER EEID, A. M. 

12mo. 572 pages. Price $1 00. 

This work, which is designed for schools, contains the PRONUNoiATioa 
and Explanation of all English words authorized by eminent writers. 

A Vocabulary of the roots of English words. 

An Accented List of Greek, Latin, and Scripture proper names. 

An Appendix, showing the pronunciation of nearly 8,000 of the 
most important Geographical names. 

It is printed on fine paper, in clear type, strongly bound. 

And is unquestionably one of the best dictionaries for the se'hool- 

room extant. 

Ffom C. S. Henky, Professor of PMlsosophy, History^ and Belles- Lettres, in the 
University of the City of New York. 

"Keid's Dictionary of the English Language is an admirable book foi the jse ol 
schools. Its plan combines a greater number of desirable conditions for such a work, 
than any with which I am acquainted ; and it seems to me to be executed in geni-rai 
with great judgment, fidelity, and accuracy.'' 

From IIeney Eeed, Professor of English Literature in the University of Peniisji- 

vania. 

"Keid's Dictionary of the English Language appears to have been compiled upon 
cound principles, and with judgment and accuracy. It has the merit, too, of combining 
much more than is usually looked for in dictionaries cf small size, and will, I believe, 
be found excellent as a convenient manual for general reference, and also for v*'riouE 
purposes of education." 



GRA^HAM'S ENGLISH SYNONYMS, 
CLASSIFIED AND EXPLAINED; 

WITH PRACTICAL EXERCISES. DESIGNED FOR SCHOOLS AND PRIVATE TU««0» 
WITH AN INTRODUCTION AND ILLUSTRATIVE AUTHORniES. 

BY HENRY REED, LL. D. 
1 Vol. 12mo. Price $1 00. 

This is one of the best books published in the department of Ian 
guage, and will do much to arrest the evil of making too common us« 
of inappropriate words. The work is well arranged for classes, anci 
can be made a branch of common school etudy. 

It is admirably arranged. The Sjnionyms are treated with re^erenca 
to their character, as generic and specific ; as active and pasFive; fta 
positive and negative; and as miscellaneous synonyms. 



I). APPLETON §- CO., PUBLISHERS. 

HAND-BOOK OF THE ENGLISH LANGUAGE 

BY G. E. LATHAM, M. D., F. R. S. 
l2mo. 400 pages. Price $1 25. 

This work is designed for the use of students in the University iiuU 
High Schools. 

" His work is rigidly scientific, and hence possesses a rare valua. With the wide- 
spreading growth of the Anglo-Saxon dialect, the immense present and prospective 
power of those with whom this is their ' mother tongue,' such a treatise must be counted 
alike interesting and useful." — Watchman and Reflector. 

"A work of great research, much learjiing, and to every thmking scholar it will be a 
Dook of study. The Germanic origin of the English language, the affinities of the Eng 
teh with other Languages, a sketch of the alphabet, a minute investigation of the etymo* 
ogy of the language. &c.. of great value to every philologist" — Obserner. 



HISTORY OF ENGLISH LITERATURE. 

BY WILLIAM SPALDING, A. M. 

FBOFESSOR OF LOGIC, RHETORIC, AND METAPHYSICS, IN THE UNIVERSITY OP ST. ANDREWS 

12mo. 413 pages. Price $1 00. 

The above work, which is just published, is offered as a Text-book 
for the use of advanced Schools and Academies. It traces the literary 
progress of the nation from its dawn in Anglo-Saxon times, down to 
the present day. Commencing at this early period, it is so constructed 
as to introduce the reader gradually and easily to studies of this kind. 
Comparatively little speculation is presented, and those literary monu- 
ments of the earlier dates, which were thought most worthy of atten 
tion, are described with considerable fulness and in an attractive 
manner. In the subsequent pages, more frequent and sustained efforts 
are made to arouse reflection, both by occasional remarks on the rela- 
tions between intellectual culture and the other elements of society, 
and by hints as to the theoretical laws on which criticism should bt 
founded. The characteristics of the most celebrated modern works are 
analyzed at considerable length. 

The manner of the author is remarkably plain and interesting, 

almost compelling the reader to linger over his pages with unwearied 

attention. 

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U. APPLE TON ^ CO., PUBLISHERS. ^^ 

CLASS-BOOK OF CHEMISTRY. 

BY EDWAED L. YOUMANS. 

12mo. 340 Pages. Price 75 Cents. 

Every page of this book bears evidence of the author's supeiioi' 
ability of perfectly conforming his style to the capacity of youth. This 
is a merit rarely possessed by the authors of scientific school-books, 
and will be appreciated by every discriminating teacher. It is espe 
cially commended by the eminently practical manner in which each 
subject is presented. Its illustrations are drawn largely from the phe- 
nomena of daily experience, and the interest of the pupil is speedily 
awakened by the consideration that Chemistry is not a matter belong- 
ing exclusively to physicians and professors. 

From Prof. "Wm. H. Bigelow, Principal of Clinton Street Academy. 
" The eminently practical character of the Class-Book treating of the familiar ap- 
plications of the science, is in my opinion its chief excellence, and gives it a value fai 
superior to any other work now before the public." 

From David Syme, A. M., formerly Principal of the Mathematical Department., 
and Lecturer in- Natural Philosophy, Chemistry and Physiology, in Columbia Col 

" Mr. Youmans : Dear Sir, — I have carefully examined your Class-Book on Chem- 
istry, and, in my opinion, it is better adapted for use in schools and academies than any 
other work on the subject that has fallen under my observation. 

" I hope that the success of your Class-Book will be proportionate to its merits, and 
that your efforts to diffuse the knowledge of Chemistry will be duly appreciated by the 
friends of education." 

" Either for Schools or for general reading, we know of no elementary work on 
Chemistry which in 3vcry respect pleases us so much as this." — Com. Advertiser, 



CHART OF CHEMISTRY. 

BY EDWAED L. YOUMANS. 

"Youmans' Chart of Chemistry" accomplishes for the first time, fov 
chemistry, what maps and charts have for geography, astronomy, geo- 
logy, and the other natural sciences, by presenting a new and admir- 
able method of illustrating this highly interesting and beautiful science. 
Its plan is to represent chemical compositions to tlio eye by colored 
diagrams, the areas of which express proportional quantities. 

ABOVE, IN ATLAS FORM, Nearly Ready. 

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